Second International Conference on
Network Analysis 2012
May 7th – May 9th, 2012
Center for Applied optimization (CAO),
University of Florida, USA
Laboratory of Algorithms and Technologies for Networks Analysis
(LATNA), Higher School of Economics, Russia
Second International Conference in Network Analysis
2.
Monday, May 7th
Room 313 HSE, 25/12 Bolshaya Pecherskaya Str.
15:00-15:30 Panos M. Pardalos
Second International Conference on Network Analysis 2012
15:30-16:20 Christodoulos A. Floudas
Towards Large Scale Deterministic Global Optimization
16:20-16:40 Coffee Break
16:40-18:10 Session 1
Ludmila Egorova
Behavioral model of stock exchange
Dmitry Malyshev
On expanding operators for the independent set problem
Dmitry Mokeev
Structural and complexial properties of P3-könig graphs
Victor Zamaraev
A heuristics for the weighted independent set problem
2
Second International Conference in Network Analysis
2.
Tuesday, May 8th
Room 313 HSE, 25/12 Bolshaya Pecherskaya Str.
10:00-10:50 Boris Mirkin
Representing Activities by Taxonomy Concepts: Clustering and Lifting
10:50-11:10 Coffee Break
11:10-12:30 Session 1
Pando G. Georgiev
Innovative tools for analyzing state transitions and evolution of complex dynamic networks
Alexey Yashunsky
Using Online Social Networks for Social Geography Studies
Alexander Rubchinsky
A New Algorithm of Network Decomposition and its Application for Stock Market Analysis
12:30-14:00 Lunch Break
14:00-14:50 Ding-Zhu Du
Min-Weight Connected Sensor Cover and Max-Lifetime Target Coverage
14:50-15:50 Session 2
Anton Kocheturov
Market Graph Analysis by Means of the P-Median Problem
Mikhail Batsyn
Applying Tolerances to the Asymmetric Capacitated Vehicle Routing Problem
Evgeny Maslov
Complex approach to solving the maximum clique problem
15:50-16:10 Coffee Break
3
Second International Conference in Network Analysis
2.
16:10-17:30 Session 3
Grigory Bautin
Markov chains in modeling of the Russian financial market
Dmitry Gorbunov
Simulation of Pedestrian Crowds with Anticipation using Cellular Automata Approach
Pankaj Kumar
Behavioural Dynamics in Stock Market
Lazarev Evgeny Alexandrovich
Bi-criteria model and algorithms of solving data transmission network optimization problem
4
Second International Conference in Network Analysis
2.
Wednesday, May 9th
Room 313 HSE, 25/12 Bolshaya Pecherskaya Str.
9:30-10:20 Mauricio G. C. Resende
Randomized Algorithms for the Handover Minimization Problem in Wireless
Network Design
10:20-10:40 Coffee Break
10:40-12:20 Session 1
D.V. Kasatkin
Synaptic cellular automaton for description the sequential dynamics of excitatory neural
networks
Pavel Sukhov
Heuristic Algorithm for the Single Machine Scheduling Problem
Ilya Bychkov
“Patterns” for solving the Cell Formation Problem
Peter Koldanov
Statistical Properties of the Market Graph
12:30-14:00 Lunch Break
5
Second International Conference in Network Analysis
2.
Towards Large Scale Deterministic Global Optimization
Christodoulos A. Floudas
Department of Chemical and Biological Engineering
Princeton University, USA
floudas@princeton.edu
In this seminar, we will provide an overview of the research progress in deterministic global
optimization. The focus will be on important contributions during the last five years, and will
provide a perspective for future research opportunities. The overview will cover the areas of (a)
twice continuously differentiable constrained nonlinear optimization, and (b) mixed-integer
nonlinear optimization models. Subsequently, we will present our recent fundamental advances
in (i) convex envelope results for multi-linear functions, and edge concave functions, (ii) a
piecewise quadratic convex underestimator for twice continuously differentiable functions, (iii)
piecewise linear relaxations of bilinear functions, (iv) large scale extended pooling problems,
and (v) large scale generalized pooling problems. Computational studies on medium and large
scale global optimization applications will illustrate the potential of these advances.
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Second International Conference in Network Analysis
2.
Behavioral model of stock exchange
Fuad Aleskerov, Lyudmila Egorova
National Research University Higher School of Economics, Moscow, Russia
alesk@hse.ru, legorova@hse.ru
Due to the global financial crisis and its consequences stock exchange nowadays is an essential
element of market infrastructure, a sensitive "barometer" to the slightest changes in the economy.
For this reason the importance of the study of the stock exchange processes and the construction
of adequate models of the exchange game has been increased. Behavioral finance is a new
direction in financial economics, which explains the trading process based on investor
psychology and the impact of their behavior on the market. Recently Taleb N.N. suggested to
analyze the crises (called Black Swans) as the events with three main properties. A Black Swan
is a very rare event, it carries an extreme impact, and the occurrence of this event cannot be
predicted in advance (and only after the Black Swan happened we can come up with its
explanation). Thus, the Black Swan is a metaphor for the crisis itself. Therefore everyone has to
expect these Black Swans and be ready for their occurrence. However, should all investors
follow such a strategy? And should we expect a rare and unpredictable event, even with a big
impact, rather than deal with “the bird in the hand”?
To answer this question we construct a mathematical model of the stock exchange, in which the
processes are modeled as a reaction to the signals about the state of the economy. There are two
Poisson flows of signals/events of two types, one of which is 'regular' event that corresponds to a
stable economy and the second one is the 'crisis' event signaling about the crisis. The intensity of
the first flow is much greater than the intensity of the crisis events (Black Swans rarity
condition). The player does not know in advance about the type of the incoming signal and have
to recognize it (the condition of unpredictability). Player’s wealth depends on how well she
identifies the signals on the stock exchange, because gain/loss from the crisis event is much
greater than the gain/loss in case of the ordinary, frequent events (condition of great influence).
We showed that the average player's gain will be positive if she can correctly recognize the
ordinary events in slightly more than in the half of the cases. In other words, players do not need
to play more sophisticated games, trying to identify crises events in advance. This conclusion
resembles the logic of precautionary behavior, that prescripts to play the game with almost
reliable small wins. We believe that this very phenomenon lies in the basis of unwillingness of
people to expect crises permanently and to try recognizing them. The proposed model was tested
on stock exchange indices (S&P 500, Dow Jones, САС 40, DAX, Nikkei 225, Hang Seng, on
time interval 1999-2009) and on data of different shares (Microsoft, General Electric, Morgan
Chase, Proctor&Gamble, Johnson&Johnson, Apple, AT&T, IBM, Bank of America).
Acknowledgement. We are grateful for partial financial support of the HSE International
Laboratory of Decision Choice and Analysis (DeCAn Lab) and NRU HSE Science Foundation
(grant № 10-04-0030). Lyudmila Egorova expresses sincere gratitude to the HSE Laboratory of
Algorithms and Technologies for Networks Analysis (LATNA) for partial financial support.
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Second International Conference in Network Analysis
2.
On expanding operators for the independent set problem
Malyshev Dmitry Sergeevich
National Research University Higher School of Economics,
National Research University Lobachevky State University of Nizhniy Novgorod, Russia
dmalishev@hse.ru
All considered graphs are simple, i.e. undirected unlabeled graph without loops and
multiple edges. A class of graphs is a set of simple graphs. A class of graphs is called hereditary
if it is closed under deletions of vertices. It is known that a hereditary (and only hereditary class)
X can be defined by a set of its forbidden induced subgraphs Y , i.e. graphs that don't belong to
X . It is denoted by X  Free(Y ) .
Let П be an NP-complete graph problem. A hereditary graph class X is called П -easy
if П is polynomial-time solvable for graphs in X . All known to the author proofs of papers on
expansions of cases with polynomial-time solvability substantially use a specific character of the
old, narrower case. At the same time, it would be desirable to have «universal» such kind
generalizations. For the family of hereditary graph classes it is offered to consider
transformations f : S  S ' (one- or many-variable function with arguments in a part of S ),
such that Free( S )  Free( S ' ) and from П -easiness of Free(S ) follows that Free(S ' ) is also
П -easy. We will refer such kind transformations to П -expanding operators.
The case, when П is the independent set problem and S  {P5 , C5 , G} , will be only
considered further. The interest in hereditary subclasses of Free({P5 , C5 , G}) is conditioned by
several causes. Firstly, if | V (G ) | 4 , then the independent set problem is polynomial-time
solvable in Free({G}) if and only if G is a forest. Moreover, the case G  P5 is unique among
all connected graphs with five vertices with open computational status of the problem for
Free({G}) . There are many papers in which one or more forbidden induced subgraphs are added
to G  P5 and the effective solvability of the problem for obtained graphs class is proved.
Secondly, for any graph G with at most five vertices, G  P5 and G  C5 , the problem admits a
polynomial-time algorithm for graphs in Free({P5 , G}) . Unfortunately, its complexity is
unknown for the class Free({P5 , C5 }) .
Two concrete expanding operators for the independent set problem will be specified
further.
The
product
of
and
is
the
graph
G1  G2
G1
G2
(V (G1 )  V (G2 ), E(G1 )  E(G2 )  V (G1 )  V (G2 )) . It is easy to see that the mapping
{G}  {G  K1} is an expanding operator for the problem. Two more such operators are
described below.
Theorem. The mapping {P5 , C5 , G}  {P5 , C5 , G  K1} is an expanding operator for the
p
independent
set
problem.
For
any
natural
the
mapping
{P5 , C5 , G}  {P5 , C5 , G  O2 , G  K1, p } is an expanding operator for the independent set
problem.
The author is partially supported by LATNA Laboratory, NRU HSE, RF government
grant, ag. 11.G34.31.0057, by Russian Foundation for Basic Research, grants 11-01-00107-а и
12-01-00749-а, and by Federal Target Program «Academic and educational specialists of
innovative Russia», state contract 16.740.11.0310
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Second International Conference in Network Analysis
2.
Structural and complexial properties of P3-könig graphs
D. B. Mokeev
National Research University Lobachevky State University of Nizhniy Novgorod, Russia
mokeevDB@mail.ru
Hereditary class of graphs in which maximum number of non-intersecting P3-subgraphs is equal
with minimum number of vertexes contains in every such subgraphs and polynomial recognition
algorithm for this class are described.
9
Second International Conference in Network Analysis
2.
A heuristics for the weighted independent set problem
B.I. Goldengorin1, D.S. Malyshev1,2, P.M. Pardalos1,3, V.A. Zamaraev1,2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhniy Novgorod, Russia
2
National Research University Lobachevky State University of Nizhniy Novgorod, Russia
3
Center for Applied Optimization, University of Florida, Gainesville, USA
b.goldengorin@rug.nl, dmalishev@hse.ru, p.m.pardalos@gmail.com, vzamaraev@hse.ru
1
In this paper we design a new heuristic tolerance-based algorithm for solving the Weighted
Independent Set problem (the WIS, for short). Our algorithm is based on the polynomially
solvable special case of the WIS, which is defined on trees (the WIST, for short). We show that
an optimal solution and all tolerances with respect to this solution of the WIST might be
simultaneously found by the adjusted Chen et al. dynamic programming algorithm in O(n) time.
Based on this procedure we offer a heuristic algorithm for the WIS, which takes O(mnlog(m))
time. We also present several computational experiments for its approximation ratio, they
showed good enough results for some models of sparse graphs.
The authors is partially supported by LATNA Laboratory, NRU HSE, RF government grant, ag.
11.G34.31.0057. This study comprises research findings from the ‘Calculus of tolerances in
combinatorial optimization problems: theory and algorithms’ Project carried out within The
Higher School of Economics’ 2012 Academic Fund Program.
10
Second International Conference in Network Analysis
2.
Representing Activities by Taxonomy Concepts: Clustering and Lifting
Boris Mirkin
National Research University Higher School of Economics, Moscow RF
Birkbeck University of London, London UK
bmirkin@hse.ru
Given a taxonomy of a domain, the activities of an organization in the domain can be represented
by crisp or fuzzy clusters of the corresponding taxonomy leaf concepts (thematic clusters). To
represent a thematic cluster in the taxonomy, a parsimonious lifting method is developed. The
method maps the cluster’s topics to higher ranks of the taxonomy tree. The lifting criterion
involves a penalty function summing penalties for the "head" subjects together with penalties for
emerging gaps and offshoots. The developments are illustrated by using synthetic and real-world
data.
11
Second International Conference in Network Analysis
2.
Innovative tools for analyzing state transitions and evolution of complex
dynamic networks
Pando G. Georgiev and Panos M. Pardalos
Center for Applied Optimization
University of Florida, Gainesville, USA
pandogeorgiev@ufl.edu, p.m.pardalos@gmail.com
The problem of detection and prediction of changes (state transitions), dependences and
causalities in the evolution of complex networks is of tremendous significance. Several
important practical networks desperately need tools for prediction, for instance: in biological
networks - epileptic brain networks for prediction of epileptic seizures; in power system
networks - electric grid, for prediction of blackouts; in social networks - for prediction of
malicious behaviors of some social groups, etc.
We present several innovative tools applicable to this problem:
1) Reproducing Kernel Banach Spaces.
We extend the idea of Reproducing Kernel Hilbert Spaces to Banach spaces (and beyond),
developing a theory without the requirement of existence of semi-inner product (which
requirement is already explored in another construction of RKBS). We apply our construction to
the basic learning algorithms, including support vector machines, kernel regression, kernel
principal component analysis. We demonstrate the better adaptive features of such spaces to new
dimensionality reduction techniques and to detection of state transitions in some complex
networks, as epileptic brain. We introduce a qualitative new concept ”multiple reproducing
kernels”, which encompasses not only bivariate, but also multivariate connections between data
variables, arranging them in a kernel tensor - a generalization of the kernel matrix.
2) Tensor decompositions.
Multi-way structures of the data has been widely ignored in many fields of research, especially
in dynamical complex networks. The functional MRI is another typical example, where the data
is inheritably tensorial. Collapsing some of the modes to form of a matrix or vector leads to loss
of information. Many tensor representations admit uniqueness of the decomposition without
additional constraints such as orthogonality (as in Singular value decomposition, or PCA) or
independence (as in Independent Component Analysis). We review some tensor decomposition
methods and introduce new ones, involving sparsity, suitable for complex sparse networks.
3) Adaptive multi-class learning problems.
We generalize the main task of statistical learning theory to multiclass learning problems,
allowing several classes approximating functions to choose adaptively from several classes of
data (possibly heterogeneous).
4) Nonlinear skeletons of data sets and skeleton classifiers.
A particular case of multiclass learning problems is the problem of subspace clustering, which
we extend to RKBS defining in such a way the concept of nonlinear skeletons and its derivative,
Skeleton Classifier.
5) Trajectory reconstruction.
Square roots, or more generally, iterative roots of operators are of interest in dynamical systems,
chaos and complexity theory and also in the modeling of certain industrial and financial
12
Second International Conference in Network Analysis
2.
processes. An operator f acting from a set X to X, satisfying the functional equation f(f(x)) =
F(x) (for every x from X) is called ”square root” of the given operator F acting from X to X. The
problem of computing square roots of operators (if exists) remains a hard task. While the theory
of functional equations provides some insight for the iterative roots of real and complex valued
functions, iterative roots of mappings in high dimensional spaces are almost not studied and
there are little contributions to numerical algorithms for their computation. We prove existence
of iterative roots of a certain class of monotone mappings in Hilbert spaces, generalizing the
scalar case result for strictly monotone functions. We demonstrate how methods based on neural
networks and statistical learning theory can find square roots of trajectories of certain dynamical
systems.
13
Second International Conference in Network Analysis
2.
Using Online Social Networks for Social Geography Studies
Alexey Yashunsky1 and Nadezda Zamiatina2
Keldysh Institute of Applied Mathematics, Russia
2
Geography Department, Moscow State University, Russia
yashunsky@keldysh.ru, nadezam@mail.ru
1
Research in social and economic geography more often than not relies on various statistics as
raw data. Hence, the lack of trustworthy and detailed statistical materials may become a
hinderance. Whereas developed countries (e.g. USA, EU countries) have vast statistic databases
open to the public, the emerging economies and developing countries to this day still have very
limited statistical information available.
This statistical vacuum forces researchers to look for other sources of information. These can be
found, for instance, within online social networking services. Although this information is hardly
representative of the entire population and never absolutely trustworthy, it can still be used to
study certain social groups.
These research techniques may be of interest even for developed countries for studying
phenomena that are not reflected by official statistics.
We have recently carried out some basic research on "knowledge spillover" in modern Russia
using public data from the vk.com social network. The studied cases revealed some interesting
spacial patterns in the origin and later employment locations of several Russian Universities'
students. Further and deeper analysis may allow identification of the so-called bonding and
bridging connections for Universities and trace their spacial components so as to evaluate their
influence on creative and labor force migrations in modern Russia.
The challenges for network analysis in this area are both technical and theoretical. On the one
hand, processing social network data with geographical goals requires the development of
specific tools, on the other hand, formal network-level criteria could help the identification of
certain geography-specific phenomena.
14
Second International Conference in Network Analysis
2.
A New Algorithm of Network Decomposition and its Application for Stock
Market Analysis
1
Boris Goldengorin1, Panos Pardalos1,2, Alexander Rubchinsky1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia
2
Center for Applied Optimization, University of Florida, Gainesville, USA
b.goldengorin@rug.nl, p.m.pardalos@gmail.com, arubchinsky@yahoo.com
The network decomposition problem is one of the well-known «classical» problems of network
analysis. Informal character and great diversity of applications have led to many different formal
statements of the problem. The essence of the suggested approach consists in a new combination
of two known ideas: finding a cut by the so called frequency method and checking statistical
stability of obtained divisions. In both directions new modifications are suggested.
The algorithm is constructed as a multistage procedure. A result of every stage is a family of
decompositions that firstly is gradually expanded and after gradually contracted so that the
output of the entire procedure consists of one decomposition.
The essential features of the suggested approach are formulated as follows.
1. The number of parts is determined by the algorithm itself. Particularly, the algorithm can
establish the absence of reasonable divisions (at least, in the framework of the suggested
method).
2. The output can produce not only decompositions but single parts and their families as well.
3. There are only few (for such a universal scheme) meaningful parameters.
The approach is applied to analysis of data from stock markets of USA, Sweden and Russia. The
only input data consists of all the pairwise correlations between prices of stocks. The network is
constructed as follows. Its vertices correspond to stocks; any vertex is connected to 4 closest
(with the maximal correlation coefficients) vertices. Stable clusters were revealed in USA and
Russian stocks. They correspond to firms engaged in the same or close kinds of activity (for
instance, in USA in gold mining and investment, in Russia in electricity production). In Sweden
market the algorithm does not reveal stock clusters.
15
Second International Conference in Network Analysis
2.
Min-Weight Connected Sensor Cover and Max-Lifetime Target Coverage
Ding-Zhu Du
University of Texas at Dallas, USA
dzdu@utdallas.edu
It was open for many years whether the target coverage problem has a polynomial-time constantapproximation or not. In this talk, we introduce a solution, 3.65-approximation, which is a new
result in our research group in UTD (University of Texas at Dallas).
The target coverage problem can be stated as follows:
Suppose each sensor has unit lifetime and a unit disk as its coverage area. Given a set of targetpoints and a set of sensors in the Euclidean plane, find a sensor sleep/activate schedule to
maximize the lifetime under constraint that every target-point is monitored by at least one sensor
during the lifetime. This constant-approximation is established by its connection to minimum
weight connected sensor cover problem.
16
Second International Conference in Network Analysis
2.
Market Graph Analysis by Means of the P-Median Problem
Mikhail Batsyn1, Boris Goldengorin1, Anton Kocheturov1, Panos Pardalos1,2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia
2
Center for Applied Optimization, University of Florida, Gainesville, USA
mbatsyn@hse.ru, b.goldengorin@rug.nl, antrubler@gmail.com, p.m.pardalos@gmail.com
1
In this work we apply pseudo-Boolean approach to analysis of stock market graphs. We divide
market graphs into clusters of highly correlated stocks by means of the p-Median model and
search for regularity in the calculated results. Our final goal is to provide a new tool for a deeper
understanding of the market structure dynamics.
17
Second International Conference in Network Analysis
2.
Applying Tolerances to the Asymmetric Capacitated Vehicle Routing Problem
1
Mikhail Batsyn1, Boris Goldengorin1, Panos Pardalos1,2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia
2
Center for Applied Optimization, University of Florida, Gainesville, USA
mbatsyn@hse.ru, b.goldengorin@rug.nl, p.m.pardalos@gmail.com
In this talk we consider the Asymmetric Capacitated Vehicle Routing Problem (ACVRP). We
solve the ACVRP with two different versions of branch-and-bound algorithm. The first one is
the classical branch-and-bound algorithm which uses the cost-based branching rule. The second
one is a new branch-and-bound algorithm in which we first take the branch which has the
minimal tolerance. Such a tolerance-based approach was suggested by Boris Goldengorin,
Gerard Sierksma and Marcel Turkensteen (2004) and proved its efficiency for the Asymmetric
Travelling Salesman Problem (ATSP). We compare the number of search tree nodes and
computational times for these two algorithms on several ACVRP instances and show that
tolerance-based branching rule is more efficient.
We also present a new heuristic algorithm for the ACVRP which can be related to the class of
cluster-first route-second heuristics. On the first stage the vertices are divided into K clusters by
solving the Capacitated P-Median Problem so that all the vertices from one cluster can be visited
by one of the K vehicles. This problem is solved exactly by means of the pseudo-Boolean pmedian model suggested by Boris Goldengorin and his co-authors in 2009-2011. On the second
stage the ATSP problem is solved exactly for each cluster again using a tolerance-based
approach. After these two stages we iteratively move vertices between the found routes while the
objective function is improved. Among all the vertices we move that vertex from one route to
another, for which this movement is feasible and the improvement of the objective function is
maximal.
18
Second International Conference in Network Analysis
2.
A Combined Approach to Solving the Maximum Clique Problem
Mikhail Batsyn1, Boris Goldengorin1, Evgeny Maslov1, Panos Pardalos1,2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia
2
Center for Applied Optimization, University of Florida, Gainesville, USA
mbatsyn@hse.ru, b.goldengorin@rug.nl, lyriccoder@gmail.com, p.m.pardalos@gmail.com
1
In this talk we suggest a combined approach to solving the Maximum Clique Problem (MCP). It
is based on two classical NP-hard combinatorial optimization problems: the Graph Coloring
Problem (GCP) and the Maximum Independent Set Problem (MISP). We use heuristic solutions
of these problems to improve the performance of our exact algorithm. Following the MCS
algorithm (Tomita, Sutani, Higashi, Takahashi and Wakatsuki, 2010), graph coloring is used as a
branching strategy for finding the maximum clique. A heuristic solution of the MISP for the
complement graph returns a good lower bound for the MCP and improves the performance of the
algorithm. Moreover, if colors are first assigned to those vertices which are in the large cliques,
then the large search sub-trees related to such vertices are pruned due to the small color numbers.
We have also improved the sequential graph coloring suggested by Tomita, Sutani, Higashi,
Takahashi and Wakatsuki (2010). We illustrate our findings by means of a computational study
for the MCP.
19
Second International Conference in Network Analysis
2.
Markov chains in modeling of the Russian financial market
Grigory Bautin and Valery Kalyagin
Laboratory of Algorithms and Technologies for Network Analysis
National Research University Higher School of Economics, Nizhny Novgorod, Russia
greg.bautin@gmail.com, vkalyagin@hse.ru
We consider a Markov chains model for the problem of multiperiod portfolio optimization, and
apply it to the Russian stock market. Due to higher volatility and other peculiarities of the
Russian market, the known approaches produce the phenomena of non stability. We propose
enhancements to the model in order to smooth it.
20
Second International Conference in Network Analysis
2.
Simulation of Pedestrian Crowds with Anticipation using Cellular Automata
Approach
Mikhail Batsyn1, Boris Goldengorin1, Dmitry Gorbunov1, Panos Pardalos1,2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia
2
Center for Applied Optimization, University of Florida, Gainesville, USA
mbatsyn@hse.ru, b.goldengorin@rug.nl, dmigorbunov@gmail.com, p.m.pardalos@gmail.com
1
Recently, cellular automata have been applied to models of traffic and evacuation without mental
properties. Goldengorin, Krushinsky and Makarenko have shown that three criteria namely the
minimization of evacuation time, maximization of instantaneous flow of pedestrians, and
maximization of mentality-based synchronization of a crowd are interdependent. In this talk we
discuss our implementation of this model and its potential application to study networks of
neurons.
21
Second International Conference in Network Analysis
2.
Behavioural Dynamics in Stock Market
Pankaj Kumar
Perm State National Research University, Russian Federation
kumar.x.pankaj@gmail.com
Stock market is an example of complex system, which is characterized by a highly intricate
organization and the emergence of collective behaviour. In this paper, we quantify this
behavioural dynamics in the stock market by using concepts of network synchronization. We
consider networks constructed by the correlation matrix of asset returns and study the time
evolution of the phase coherence among stock prices. It is verified that during financial crisis a
synchronous state emerges in the system, defining the market's direction. Furthermore, the paper
proposes a statistical regression model able to identify the network topological features that
mostly influence such an emergence. The coefficients of the proposed model indicate that the
average shortest path length is the measurement most related to network synchronization.
Therefore, during economic crisis, the stock prices present a similar evolution, which tends to
shorten the distances between stocks, indication a collective behavioural dynamics.
22
Second International Conference in Network Analysis
2.
Bi-criteria model and algorithms of solving data transmission network
optimization problem
Lazarev Evgeny Alexandrovich, Misevich Pavel Valerievich, Shaposhnikov Dmitry Evgenievich
Nizhny Novgorod State Technical University n.a. R.E. Alexeev, Nizhny Novgorod, Russia
elazarev.nnov@gmail.com, p_misevich@mail.ru, dm.shaposhnikov@gmail.com
A data transmission network model based on classic network-flow models is proposed.
Consider acyclic oriented graph G  V , E  , describing existing data transmission network.
Vertices of the graph represent multiplexers of the network. Edge
u, v  E connects vertices
cu, v  . Two vertices of the
u and v , represents the data channel and has positive capacity
graph s and t are considered information source and sink respectively.
The set E ( E  E    ) describes data channels which can be added to the network.
The capacity cu, v  and construction cost pu , v  is given for each edge u, v   E  .
The amount of information which can be transmitted over the data channel per time unit
is defined by the flow function f : V V   ( f u , v  describes the flow between vertices
u and v ).
It is necessary to modify existing network by construction some channels of the set E to
increase the maximum network flow. A possible solution x of the problem is a set of edges
E *  E  . Two optimization criteria are considered:
1.
2.
The cost of data channels construction: Q1  x  
The maximum network flow: Q2  x  

described by the graph G  V , E  E
*
*
.
 pu, v 
( u ,v )E *
 f s, v ,
vV
Optimization problem: for given acyclic oriented graph
edges E  E  E     , capacity matrices
G  V , E  and the set of
cu, v  , c u, v  and construction cost matrix
pu, v  find the set of Pareto-optimal solutions of problem min Q1  x , max Q2  x  .
xD
xD
It is proven that cardinality of the Pareto-optimal solutions set can have exponential
dependence on the problem dimension (cardinality of E ). Also, it is proven that the problem is
NP-hard (the knapsack problem is polynomially reduced to the considered problem).
Taking into account assumption that P  NP and computational difficulty of the problem
heuristic methods are proposed to find sub-optimal solutions for the considered problem. The
paper presents exact algorithms based on branch and bound method, heuristic algorithms based
on genetic algorithms and simulated annealing algorithm and results of computational
experiments.
23
Second International Conference in Network Analysis
2.
Randomized Algorithms for the Handover Minimization Problem in Wireless
Network Design
Mauricio G. C. Resende
Algorithms & Optimization Research Department
AT&T Labs Research
Shannon Laboratory, Florham Park, New Jersey, USA
mgcr@research.att.com
Mobile wireless devices connect to an antenna tower to which it has a strong signal. As the
device moves it may connect to a sequence of towers. The process that takes place when a
device changes the tower to which it is connected to is called handover (or handoff). Handovers
are not done by the tower itself but rather by the radio network controller
(RNC) to which the tower is connected. Each tower has associated with it a traffic level which
depends, for example, on where it is located. One or more towers can connect to an RNC but
each RNC can handle a maximum amount of traffic thus limiting the subsets of towers that can
connect to it. Handovers between towers connected to different RNCs tend to fail more often
than those between towers connected to the same RNC.
Handover failure causes a dropped call which one would prefer to avoid.
Therefore minimizing the number of handovers between towers connected to different RNCs
may lead to a more reliable level of wireless service.
Given a set of towers, each with a given amount of traffic, a set of RNCs, each with a given
capacity, and a matrix specifying the number of handovers between pairs of towers, the
HANDOVER MINIMIZATION PROBLEM (HMP) seeks an assignment of towers to RNCs
such that the RNC capacity is not violated and the number of handovers between towers
connected to different RNCs is minimized.
We describe three randomized heuristics for solving the HMP. The first is a GRASP with pathrelinking for the generalized quadratic assignment problem. The other two are specially tailored
for the HMP. One is is a GRASP with evolutionary path-relinking and the other is a biased
random-key genetic algorithm.
We compare these heuristics on a set of randomly generated instances as well as on real-world
networks from a large wireless provider.
24
Second International Conference in Network Analysis
2.
Synaptic cellular automaton for description the sequential dynamics of
excitatory neural networks
1
D.V. Kasatkin1, A.S. Dmitrichev1, V.I. Nekorkin1,2
Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia
2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhniy Novgorod, Russia
kasatkin@neuron.appl.sci-nnov.ru, admitry@neuron.appl.sci-nnov.ru,
vnekorkin@neuron.appl.sci-nnov.ru
One of the significant problems of neurodynamics is development of analytical methods for
studying of models of complex neural networks. We present an approach for analyzing the
dynamics of excitatory neural networks. It consists in reducing continuous dynamics of neural
networks to a discrete dynamical systems in the form of a cellular automaton (CA) on the graph
of connections. In the approach the main role is played by the dynamics of synapses but not by
the specific features of neurons. In fact, the CA represents a network of synapses with a finite
number of states which alternate each other according to some fixed rules. To determine the
rules one needs to study only the responses of an individual synapse onto actions of neighboring
(in graph of connections) synapses through corresponding neurons. As a result the numerical
integration of the whole system of ordinary differential equations (ODEs) is not needed.
Moreover, since the form of the neuron responses is not important, the approach is applicable to
a broad set of networks including those consisting of neurons, which possess the neural
excitability property (neurons of the class 2 excitability).
25
Second International Conference in Network Analysis
2.
Heuristic Algorithm for the Single Machine Scheduling Problem
1
Boris Goldengorin1, Panos Pardalos1,2, Pavel Sukhov1
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia
2
Center for Applied Optimization, University of Florida, Gainesville, USA
b.goldengorin@rug.nl, p.m.pardalos@gmail.com, pavelandreevith@rambler.ru
There are three single machine scheduling problems with an open computational complexity
status. One of them, the preemptive single machine scheduling problem of minimizing the total
weighted completion time with equal processing times and arbitrary release dates, will be
discussed in this talk. We are going to describe three heuristics for this scheduling problem. Two
of them are based on it's linear assignment problem reduction, and one based on the WSRPT
(weighted shortest remaining processing time) rule. Our computational experiments show that
the WSRPT rule based heuristic returns either an exact optimal or a high quality schedule.
26
Second International Conference in Network Analysis
2.
“Patterns” for solving the Cell Formation Problem
Mikhail Batsyn1, Ilya Bychkov1, Boris Goldengorin1, Panos Pardalos1,2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia
2
Center for Applied Optimization, University of Florida, Gainesville, USA
mbatsyn@hse.ru, il.bychkov@gmail.com, b.goldengorin@rug.nl, p.m.pardalos@gmail.com
1
In this paper we define the notion of a “pattern” which is closely connected with the Assignment
Problem solution and show how to apply it for solving one well-known combinatorial
optimization problem, namely the Cell Formation Problem. Our iterative algorithm is based on
flexible adjustments of the given collection of cells starting with an initial solution. The
algorithm terminates when all possible adjustments of shapes and sizes for each cell and the
current collection of all cells cannot be improved by means of the prespecified objective function
value. Sometimes such iterations may lead to patching a pair of neighboring cells or splitting
each cell in a number of cells. Experiments with the number of cells allow us to increase the
objective function values for some cell formation problem benchmark instances.
27
Second International Conference in Network Analysis
2.
Statistical Properties of the Market Graph
Valery Kalyagin1, Alexander Koldanov1, Peter Koldanov1, Panos Pardalos1,2
Laboratory of Algorithms and Technologies for Network Analysis, National Research
University Higher School of Economics, Nizhny Novgorod, Russia
2
Center for Applied Optimization, University of Florida, Gainesville, USA
vkalyagin@hse.ru, akoldanov@hse.ru, pkoldanov@hse.ru, p.m.pardalos@gmail.com
1
The paper deals with the statistical analysis of the construction method of the market graph
introduced in [Boginski, Butenko and Pardalos 2003]. The main goal of the paper is the
investigation of the optimality of the method of construction of the market graph from the
statistical point of view. According to the classical approach by Wald the optimal statistical
procedures is the statistical procedures with the minimal conditional risk in a fixed class. In our
investigation we consider the class of unbiased statistical procedures. As a statistical model of
the financial market we use the classical model by Markowitz. According to this model the
returns of financial stocks have a multivariate normal distribution defined by the vector of their
means and the covariance matrix. The market graph (true market graph) is the matrix with
entries 0 and 1, where we put 0 if the associated correlation is less then given threshold and 1
otherwise. Sample market graph is the market graph constructed from the sample correlations.
The main question discussed in this paper is the relation between true and sample market graphs.
The construction method of the market graph introduced in [Boginski, Butenko and Pardalos
2003] can be considered as a statistical procedure for the construction of the true market graph
from the sample market graph. We show that this method is optimal in the class of unbiased
multiple decision statistical procedures. To prove this result we put the problem in the
framework of Lehman theory of multiple decision statistical procedures and precise the choice of
generating hypothesis.
28