Michael Brand
July 1-3, 2014
Not to be confused
with the functional
analysis conference.
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Is a semiannual conference
Is a biannual conference
Occurs every two years
Approximately.
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Exercise #1: Complete the sequence:
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1998, 2001, 2004, 2007, 2010, 2012, 2014, ?
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Is B-ranked (CORE 2013, ERA 2010)
Submissions are from all walks of math
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Is traditionally hosted in Italy
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They don't insist on continuing with Italy, but
they do insist on holding it someplace fun.
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◦ e.g., one paper this year was from Prof. David Peleg
(dean of Math&CS at the Weizmann Institute of Science).
◦
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◦
◦
◦
◦
◦
1998:
2001:
2004:
2007:
2010:
2012:
2014:
Isola d'Elba
Isola d'Elba
Isola d'Elba
Castiglioncello (Livorno), Tuscany
Ischia (Napoli)
San Servolo Island, Venice
Lipari Island, Sicily
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1. When your paper gets accepted.
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2. When your read the program.
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3. When you realise how difficult it is to get
there.
Singapore to
Munich
Munich to
Catania
Melbourne to
Singapore
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3. When you realise how difficult it is to get
there.
Recap so far:
◦ 31 hours in so far
 With very good connections!
Time to realise that Italy has its own power plug system.
Two of them.
And that they don't believe in grounding their power.
Also, that no power converters are for sale at the Catania
airport.
◦ In fact, there's not much in Catania airport, unless you're
after gelato.
◦
◦
◦
◦
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3. When you realise how difficult it is to get
there.
◦ Next, by bus from
Catania to Milazzo,
4 hours.
◦ 5 hours, because the
bus had an accident on
the way to Catania.
◦ 6 hours, because the
bus broke down on the
way to Milazzo.
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•
•
•
•
•
But at least it broke down where we had some
good view.
Mount Etna
At over 3.3km, Europe's
tallest active volcano.
• (exact height
changes after each
eruption)
In an almost-constant
state of eruption.
One of 17 "decade
volcanoes" world-wide.
World heritage site.
Darn big.

3. When you realise how difficult it is to get
there.
◦ From Milazzo to Lipari
via hydrofoil.
◦ Note to self:
A hydrofoil two
 Never board a hydrofoil hours overdue,
due to bus
whose crew is two
problems.
hours overdue
anywhere.
◦ Time from Milazzo to
Lipari:
 1 hour
A hydrofoil
 50 minutes when in a
hurry.
A hydrofoil
in a hurry.

3. When you realise how difficult it is to get
there.
◦ Total door-to-door travel time, over 40 hours.
◦ Longer on the way back.
 Where we also had a bus breakdown.
 And switched to a GiuntaBus.
◦ Same route on the way back,
replacing Munich for Frankfurt.
◦ Note to self: Frankfurt airport
prides itself on its buggy service.
◦ Total time on the road: 85 hours.
◦ Total time on the island: 83 hours.

3. When you realise how difficult it is to get
there.
◦ And if you think that's bad, consider that this guy
only came from nearby Oman, and still managed
to spend 35 hours on the way over.
Prof. Rudolf Fleischer
Head of department of computer
science and dean of engineering,
GUTech, Oman.
Record holder for guy with the
worst connections.

4. When you find out that while getting there
is no fun at all, being there is pretty good.
Volcano Island:
Home of the
original volcano
Stromboli
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Greek influences.
Lovely canyons.
Clear, warm water.
Abundant night-life.
Hot weather, so you
are encouraged to
drink lots of wine.
Ridiculously
expensive food.
Insalata verde
4euro
approx. AU$6

5. When you realise that everyone is on a
Paolo
first-name basis.
Florian
Erik
Minghui
Giuseppe
Maaler
Fermi
Irina
Vincenzo
Rudolf
Takaaki
Erik
Giovanni
Pawel
Zsuzsanna Alfredo
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5. When you realise that everyone is on a
first-name basis.
Pascal
Aaron
There is actually a good
reason for this.
For most participants,
this isn't their first FUN.
In fact, it's almost
assumed that if you came
here once, you'll want to
come back again every
time.
Many of the participants
were in all 7 FUNs so far.
Erik
Demaine
Record
holder:
most
FUN
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Participated in all seven FUN conferences.
Co-authored 3 of the papers in this FUN
◦ Cited in, perhaps, most other papers, too.
Designed the FUN logo.
Was this year's invited speaker.
Organiser of next year's FUN.
Oh, and:
◦ His PhD thesis was on mathematical origami.
◦ My first encounter with him was seven years ago in
the context of polyomino tiling. He was a fun guru
already back then.
Erik
Demaine
Record
holder:
most
FUN

But also (among his less fun achievements):
◦ Youngest professor in the history of MIT.
◦ MacArthur fellow (and many other awards besides).
◦ Member of the Theory of Computation group at MIT
Computer Science and Artificial Intelligence
Laboratory.

6. ... that activities are somewhat unusual.
Barbara
Erik
Fermi
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6. ... that activities are somewhat unusual.
7. ... that wacky props are encouraged.
Vincenzo
Zsuzsanna
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6. ... that activities are somewhat unusual.
7. ... that wacky props are encouraged.
8. ... that dressing up is allowed.
Irina
Maaler
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6.
7.
8.
9.
...
...
...
...
that activities are somewhat unusual.
that wacky props are encouraged.
that dressing up is allowed.
as are nerdy jokes.
Giovanni
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
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6. ... that activities are somewhat unusual.
7. ... that wacky props are encouraged.
(Because, hey,
8. ... that dressing up is allowed.
you're on an
island...)
9. ... as are nerdy jokes.
10. ... and that what you get when you
register is a beach towel.

Some repeating themes:
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Greg Aloupis, Erik Demaine, Alan Guo,
Gionvanni Viglietta
Abstract:
◦ We prove NP-hardness results for five of Nintendo's
largest video game franchises: Mario, Donkey Kong,
Legend of Zelda, Metroid, and Pokémon. Our results
apply to generalized versions of Super Mario Bros.
1, 3, Lost Levels, and Super Mario World; Donkey
Kong Country 1-3; all Legend of Zelda games; all
Metroid games; and all Pokémon role-playing
games. In addition, we prove PSPACE-completeness
of the Donkey Kong Country games and several
Legend of Zelda games.
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Rules of the game remain as they are.
Maps are invented.
NP reductions from 3-SAT.
PSPACE reductions from TQBF.
Other reductions are from 'push' game
variants and from door/pressure-plate
puzzles.
Additional proofs include:
◦ Gadget-fixes against Super Mario glitches.
◦ Positive PSPACE results for memory-limited game
variants.
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Giovanni Viglietta
Optimisation prob: how many can be saved?
PSPACE-complete even for single builder/basher.
In NP if there are only polynomially many
builders, bashers and miners.
Finding maximum is APX-hard even when only
climbers are available. (Relative error 1/8.)
◦ [Cormode 2004] In P for levels with no "deadly areas"
and only climbers and floaters.
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Accounts for all game glitches.
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Most proofs involve multiple lemming-killing
contraptions (no fun), but not NP proof.
Number of lemmings polynomial; number of
player actions effectively polynomial.
Terrain changers only work for poly moves.
Total terrain changes polynomial.
At all other times, poly many lemmings follow
poly-length independent paths. Exptime
waits (full cycle) can be calculated efficiently.
Proof string: time stamps for player actions.
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Minghui Jiang, Pedro Tejada, Haitao Wang
Droplet slides to maximal extent (4
directions) after each move by the player.
Collects pearls.
ANY-MOVES-ALL-PEARLS in P
ANY-MOVES-MAX-PEARLS & MIN-MOVESALL-PEARLS -- APX-hard with NPC+FPT
decision problems.
ANY-MOVES-MAX-PEARLS 2-approximable.
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Compact graph representation of the board
and division into strongly connected
components can be done in time P.
After: solving ANY+ALL is 2-SAT, hence in P.
k+ALL, ANY+k in NP: path on graph can be
given as proof string.
Greedy algorithm for ANY+MAX can pick as
many as possible graph edges that contain
pearls, but each pearl may be counted on two
edges, hence 2-approx.
◦ APX result is for 22/21.
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Guillaume Fertin, Shahrad Jamshidi, Christian
Komusiewicz
[Friedman 2002]: NPC
Now: FPT for #corners
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n cells, l corners.
Describe each galaxy as a tiling of O(l)
rectangles (and symmetric rectangles).
Describe the rectangles as having relations in
terms of relative position and adjacency.
Enumerate over all possible descriptions.
◦ (Exponential.)
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For each description, exact dimensions can
be solved by an ILP with O(l) variables.
Time: f(l) polylog(n)
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Takashi Horyiama et al. (7 authors)
Old Western-Japanese game.
Connect point sets to (empty) triangles. No extra
turn when closing triangles (unlike dots-andboxes [Berlekamp]). Player with most triangles
wins.
Known: if getting extra turn, 1st player wins on
odd-sized point sets, tie on even.
New results:
◦ For convex sets, 1st to play wins. (Inductive proof.)
◦ NPC to determine if k triangles can be closed in the next
l turns.
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Windfall (Rudolf Fleischer, Tao Zhang)
◦ How many falling coins can Mario catch, using an
online strategy with finite look-ahead?
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Latin square completion (Kazuya Haraguchi,
Hirotaka Ono)
◦ How many cells can a simple strategy solve in
Sudoku, Futoshiki & BlockSum?
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Palash Dey, Prachi Goyal, Neeldhara Misra

Decision problem: can all cards in a given hand
be discarded? c colours, unlimited numbers.
Known:
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New:
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Proof technique:
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◦ [Demaine(s) et al.] NPC, FPT: nO(c^2) algorithm.
◦ 2O(c^2 log c) nO(1) algorithm.
◦ Exponential algo & NPC proof for newly introduced
harder variant "all or nothing UNO".
◦ Kernelisation to reduce to O(c2) numbers, followed by
use of known dynamic programming algorithm from
Demaine et al..

Erik Demaine, Fermi Ma, Erik Waingarten
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Single player in P
Cooperative multi-player is NPC
Competitive play is PSPACE-complete
Similar results for team play.
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Trivia:
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◦ Earliest known Domino set dates back to an
Egyptian tomb from ~1350 BC.
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Alam, Kobourov, Pupyrev, Toeniskoetter
Given a graph with edges labelled either
"near" or "far", colour the vertices such that
near vertices differ by at most t and far
vertices by more than t.
Studied on Archimedean & Laves lattices.
Results:
◦ Some colourable with fixed number of colours.
◦ Some require unbounded colours for specific
labelings.
◦ Some are not threshold colourable.
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Borassi et al.
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Idea: iterative refinement of heuristic bounds.
◦ Exploiting relation between eccentricity and
farness.
◦ Exploiting relation between farness and sampled
distance from arbitrary nodes. (Consider diametric
vertices.)
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Worst case: O(|V||E|).
On real graphs, requires at most 10-100
BFSs, so ~O(|E|).
◦ This was a main theme of Paolo Boldi's invited talk.
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Kevin Bacon was never central until 2014.
It was never possible to win "6-degrees"
◦ of anyone.
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The D&R of the graph (and list of centrals)
actually provides much insight on cinema history.
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Bang Ye Wu
Tree not given; only distance Oracle is used.
2n-3 queries are necessary and sufficient to
find diameter, radius & centres. (n=#leaves)
To find median:
◦ Deterministic algorithm: n log n.
◦ Randomized algorithm: expectation < 6n.
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Shoelace TSP with very old shoes (Deineko,
Woeginger)
◦ (But does this really count as straight-laced graph
theory?)
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Optimizing Airspace Closure with Respect to
Politicians' Egos (Kostitsyna, Löffler,
Polishchuk)
Pareto-optimal House allocations (Asinowski,
Keszegh, Miltzow)
◦ How many houses can ever be allocated?
◦ What makes a house unavoidable?
◦ How many separate solution sets are there?
(which is almost the same
thing as graph problems, but
with some subtle nuances.)
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Cicalese et al.
Each node in a graph becomes "influenced"
once enough of its neighbours are.
The general "influencers" problem is known
to be hard (even to approximate).
Solved here polynomially for trees, paths,
cycles and complete graphs.
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Krumke, Schwahn, Thielen
Similar to previous, but now the question is
computing optimal price given that perceived
price is affine in the purchase choices of the
neighbours.
Results:
◦
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◦
◦
Strongly polynomial if weights are nonnegative.
NP-hard otherwise.
Has pseudo-polynomial-time solution.
But cannot be approximated to any constant factor
unless P=NP.
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Keller, Peleg, Wattenhofer
Similar to previous, but now the question is
stabilization times.
Results:
◦ Exponential lower and upper bounds on
stabilization times.
◦ Example of an asymmetric-weight network with an
exponential-length cycle.
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Clearing Connections by Few Agents
(Levcopoulos, Lingas, Nilsson, Żyliński)
Swapping Labeled Tokens on Graphs
(Yamanaka et al.)
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Vincenzo Gervasi, Giuseppe Prencipe and
Valerio Volpi
A blend of Look-Compute-Move (LCM)
robotics with Hollywood lore.
Set of zombies. Set of humans. Zombie speed
increases with amount of sound emitted by
humans. Go for closest human.
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Problems investigated:
◦ Can a human gather the zombies without becoming
one himself?
 Demonstrated experiments with circular motion;
showed that there is an optimal speed.
◦ Can a human cause zombies to flock to a particular
place?
 Two-stage algorithm: gathering, then gathering plus
linear motion.
◦ ... spread the zombies? Every pair? Some pair? Split
into sub-groups?
 Various strategies tried. Results by simulation.
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Shantau Das, Paola Flocchini, Giuseppe
Prencipe, Nicola Santoro
Another LCM robotics question
What if robots can maintain a state in the
form of a colour? As a function of number of
colours?
Results show that the spin invariant is the
main constraint. One set of chameleons
(rotationally symmetric) is used to signal by
their relative distances.
Mathematical deabstractisation
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Takaaki Mizuki and Hiroki Shizuya
Motivation: very, very shy teens.
Improved protocols for securely calculating
general Boolean functions using a small
number of cards.
Resilience against players exploiting scuff
marks and rotationally not-invariant backsides.
Dishonest players (exploitation of input
format).
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Jannik Dreier, Hugo Jonker, Pascal Lafourcade
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Objective: "Woodako"
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Woodako is a hardware implementation of
Sako's secure auction.
Meant to implement Sako without use of
cryptography
◦ so that the non-mathematical public can be given
answers to questions around auction security
◦ ... that they never asked (because they're not
mathematicians)
◦ ... and the answer for which, though not reliant on
cryptography, still requires the ability to follow
complex mathematical proofs.
Interesting models for realworld situations.
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Ke Chen, Adrian Dumitrescu
A ruler with n links and maximal link-length
1 is folded into a simple case of diameter 1.
What is the minimal area of a case that can
carry all such rulers for all possible n?
Previous results (mainly by the authors) reach
an upper bound of 0.614 and a lower bound
of 0.476 for the convex case.
Nonconvex: [0.073, 0.583]
Upper bound
Lower bound (simplified)
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The Courteous Theatregoer's Problem
(Georgiou, Kranakis,Krizanc)
Jigsaw puzzles (MB)
Things so far out of the box
they don't know where the
box is.
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Burcsi, Fici, Lipták, Ruskey, Sawada
Background: indexed jumbled pattern
matching
◦ A real-world problem of much interest
(computational biology).
◦ Given a binary word w, does w have a substring
with s zeroes and t ones?
◦ Can be solved in O(1) with linear-sized index.
◦ But best known index-building algorithms are
O(n2/log n).
 One of them by same authors from FUN 2010.

The way to create a linear index is to note
that if w has two k-length prefixes with a 1s
and b 1s, respectively (w.l.o.g. a<b), then it
also contains a k-length prefix with x 1s for
every a<x<b.
◦ [Folklore]

Thus, the index only needs to include the
minima and the maxima.
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There is a unique word that matches all the
maxima precisely.
It has the property that no substring of any
length k of it has more 1s than the prefix of
the same length. We call this property prefix
normality (w.r.t. 1).
We call this word the canonical prefix normal
form representation of w (w.r.t. 1).
The unique word matching all the minima
precisely is the canonical prefix normal form
representation of w w.r.t. 0.

The rest of the paper is devoted to fun things
you can do with prefix normal words. These
include:
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Canonizing a word.
Deciding if a word is canonical.
Playing prefix normal word games.
A mechanical canonization algorithm.
... and more.
Results are not profound, but show that the
authors are really trying to think outside the
box in order to improve IJPM bounds.
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
The Harassed Waitress Problem (Harrah Essed
and Wei Threse; Italian House of Pancakes*)
Fun with Fonts: Algorithmic Typography (Erik
Demaine and Martin Demaine) -- 2nd invited
talk.
*Joe
Sawada and Aaron Williams, following Jacob Goodman.
?