LIBRARY
OF THE
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
we^'
iNsr.
OCT 30 1973
ALFRED
P.
SLOAN SCHOOL OF MANAGEMENT
MESSAGE-BASED RESPONSE ROUTING
WITH SELCUK NETWORKS
by
Kenan E _Sahin
Visiting Tssociate Professor
.
668-73
July, 1973
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
MASS. INST. TECH.
OCr 18 1973
DEWEY
MESSAGE-BASED RESPONSE ROUTING
WITH SELCUK NETWORKS
by
Kenan E Sahin
Visiting Xssociate Professor
.
668-73
July, 1973
LIBflAKY
I
HD29
no. ^(^^-13
RECFIVED
OCT
M
I.
f.
30
1973
LlLiKAHlES
Abstract
Computer-to-computer communication
in a
very large net, parallel pro-
cessing, and content-based retrieval associative memories all can be viewed
in a
broader context as the broadcast of a "to-whom-i t-may-concern" type
message and the subsequent routing of the response messages to the broadcast
Simplicity and economies
source.
in
logic and memory can be obtained if the
routing does not require site information and
is
as decentralized as possible.
We propose a procedure for such routing in a large net of modules of limited
logic and memory, with connectivity primarily to near neighbors with one-way
channels.
that
in
The procedure
is
based on the Selcuk Principle which maintains
properly constructed networks routing can be achieved with each module
basing its switching decision only on the identity of its input channel
upon which the broadcast message first arrived
-
a
strictly local
One-way channel connectivity emerges as advantageous because
it
(s)
information.
requires much
less memory and logic then two-way arrangements, while achieving nearly the
same efficiency in properly constructed nets.
071^706
Index Terms
response routing, message-based switching, parallel processing, computer communication, associative memory, content-
based retrieval, pattern recognition.
There
now
is
increasing attention being focused on computer networks
which allow computer to computer communication (10,
active resource sharing (18, 23, 27).
exemplified by the ARPA network
(7,
11,
12,
and inter-
14)
Such efforts are currently well
18,
13,
The ARPANET
23).
achieves
(18)
intercommunication not by line switching whereby dedicated paths are established between two interacting computers but by message switching
of the messages
is
really accomplished by a superimposed net of ident ical
small processors called Interface Message Processors
stored
is
in
it
An IMP has
(iMP's).
table showing shortest routes to all other IMP's.
a
updated frequently to take into account the level of traffic
Messages arrive with
it
While
leader portion indicating the address of the computer
a
some sense the ARPANET
in
1
1
actual y addresses
1
generalized situation
to all members
in a
Is
a
23).
itself to a rather restricted communication
it
identifies
A more
(4),
member sending a to-whom- it-may-concern message
net and then receiving responses from the appropriate
However, as one moves to many more members the table look-up
method of routing would quickly be impractical
(12,
18).
By the end of the
should not be surprising to see thousands and even hundreds of
thousands of various size computers hooked into
and small switching machines
specializing
in the
(IMP's).
such
In
a
a
going on in the network, presumably only
If
member Y then
super network of identical
net each computer, while
tasks of its environment, would be interested
depend on the activities of the other computers.
member X.
16,
With twenty members in the net this task can easily be solved with
ARPA schemes.
it
(4,
viewed as the prototype of computer
is
problem: one user contacting another user that
decade
the net.
in
decides to which of its channels to route the message
communication
members.
The table
When an IMP receives this message, by table look up of the
to be reached.
address
Switching
(16),
a
in
and even
Of the myriads of activities
few would be of use to
a
particular
such activities of interest always originated in a particular
a
devoted link can easily be created between
X
and Y.
However,
I
more generally activities of interest may be taking place at any one of
tine
To keep posted, member X must periodically or as the situation
members.
warrants
it,
Interrogate the remaining members.
In
other words, send to all
"to-whom- it-may-concern" messages or "general messages."
these must then be routed to X.
appropriate,
provided for each of the other members.
telephone
in a
telephony
If
responses are
Of course the same must be
The situation
net being able to ring all
analogous to any
Is
the other telephones and
The basic problem
then receive responses only from a few appropriate ones.
is
of routing.
require that the IMP's which we shall
For the solution of the task let us
call modules
rule out full
remain small and simple (limited logic and limited memory) and
relatively simple devices
of devices.
We are then left with a network of
connectivity as unwieldy.
We shall
(modules)
connected to only few of the collection
also rule out location-based addresses and the table-
look up schemes as utilized in ARPA (16, 23). With all
problem boils down to the following:
can a device
(module)
network of many many simple devices,
a
In
these restrictions the
inquiry which
initiate a general
propagated to the
is
entire net expediously and then have the responses routed to
A
It
without re-
vealing its location and without the respondents indicating their location.
In
addition, the response must travel along
to the optimum path.
then
it
If
could serve as
a
IV
path that
is
reasonably close
the problem can be solved with a practical
scheme,
basis for very large computer communication networks.
Another context for the same problem
exemplified by ILLIAC
a
(3,8,17,26).
In
parallel processing most notably
Is
its
current realizations there are
sixty-four processors (PE's) each connected to immediate four neighbors thus
resulting In an array of eight by eight
to
a
central processor (CU)
to all PE's and all
.
(3,
8).
Each PE
is
also connected
Instructions and data streams emanate from CU
PE's execute the Instructions
In a
lock-step fashion (3).
one
-
3
-
Transfer of data from one PE to another PE
the CU and routing worked out by the same
significant speed increases
If
in
possible but
is
As such
(26).
some classes of problems
is
mediated by
ILLIAC IVachieves
(3).
the number of PE's were to increase several fold^ very likely the
However,
present architecture would remain functional.
if
PE's were to
increase radically, say to hundred thousand or so, the CU would both be satu-
The reasonable way out would seem to be
rated, oversized and vulnerable.
further decentralization including that of routing.
a
situation similar to that which would arise
to increase significantly.
In
other words,
if the
Once again we encounter
ARPANET membership were
reasonable way of achieving the
a
advantages of parallel processing might be to equip each PE with the capability
to
"to-whom-it-may-concern" type messages,
interrogate all the others with
and then receive the appropriate response messages be they data, status
reports, new instructions, executions of instructions, etc.
If
we impose the
same restrictions on the "net" of PE's as we did on computer communication nets
we emerge with the problem stated earlier; namely, achieving message-routing
of responses to general
memory devices without
inquiries in a large net of limited-logic limiteda central
router, without complete connectivity and
without making the devices complex (which rules out table look-up schemes for
switching) yet achieving close to optimum paths for the response.
Yet another context for the same problem
is
content-based retrieval
where one desires to retrieve segments using some set of key words relayed
to all
locations, matched with contents and correct matches retrieved.
built to accomplish this task are often called associative memories
9,15,19,20,21).
key word
is
Typically memory
stored
in a
is
organized as
register of m bits.
a
Memories
(1,2,5,6,
matrix of mxn (6,20),
Either all the bits of the key
word or only some of the bits are sent through the corresponding vectors of
the memory, either serially or In parallel
(2,
6,
20).
The advantages of
The
associative memories basically derive from not having to organize memory contents and from the parallelism of the search process.
tasks that require
in
frequent interaction with memory contents these advantages would be particularly
apparent
(9,
15).
The powers of associative retrieval can be considerably enhanced by allowing for entry to and retrieval
from memory at any site
memory by allowing
in
each site to have limited logic as well as its existing limited memory.
Opera-
tionally the problem would then be achieving the propagation of "key words"
corresponding to general messages from any site to all other sites and then
routing the "responses" to the sites from where the searches
originated.
Even a more general context for the problem to be investigated
a
is
dividing
large network dynamically into subnetworks on the basis of task characteristics,
The task would be introduced from any site available.
A message containing
task characteristics would then be broadcast from that site.
Sites that accept
the characteristics would send "responses", to the broadcast source and through
response paths be linked to it.
the
still
participating
in the
Thenon the subnetwork thus formed, while
activities of the full network, could be particularly
concerned with the task at hand.
In
the abstract, all these contexts of computer communication and resource
sharing, parallel processing with decentralized control, associative memory
with entry provided at every site
in the memory,
and task-wise dynamic partition-
ing of a network reduce to the broadcast of a general message
(GM)
in a
network
and the subsequent routing of responses to the source of GM wherever the source
may be in the network.
We shall address the problem in the framework of multi-
tude of limited-logic,
limited-memory "modules" connected to adjoining neighbors
as
in
Figures 2 and
channel
is
in
3.
We shall make the connections one-way since a two-way
some sense two one-way channels and since as
the paper the one-way arrangement
is
superior.
We shall
it
will emerge in
then seek a solution to
the problem of response routing
in
such networks without resorting to central
switching and without requiring information on the locat ion (site) of GM sources
or respondents.
The basic response routing (switching)
idea Lo be explored will
be to allow for the propagation of the general message to the network as
as possible and then to have each module switch a response
on the bas
i
s
it
rapidly
may receive onl
of how the associated general message had arrived.
To obtain fundamental
transmission time of
a
results without undue complication we will
assume
message between any pair of modules to be the same.
This assumption will be realized in the network representation by making the
channels the same length.
Consequently, we will be dealing with geometrically
Furthermore, only planar networks with modules having the
regular networks.
same number of channels will be considered.
Planar geometric regularity confines us to square and hexagonal "packing".
And the equality of input output channels limits us to five classes of modules
in terms of channel
is
arrangements as shown
clockwise fashion and
in
output channel
1
"i ." derjotes
Figure
in
Labelling of channels
1.
input channel
1
whereas "o," indicates
etc.
Any network with one-way channels in which response routing without location-
based addressing
us.
is
achieved will be called
Selcuk Networks were first reported
in
discrimination and angle detection discussed
a
Selcuk Network
(24)
in
-
a
term coined by
and their application to shape
(25).
Square Class QNetwork r
Consider the Square Class
throughout only Class
us allow Module
general message.
I
C
is
Selcuk Network shown
in
Figure
modules are used and that the network
which appears
It
C
in
is
2.
Note that
connected.
Let
the center of the network to initiate the
only for convenience that we are choosing this module;
excepting for boundary conditions the results to be shown will be true for any
module
in
the network.
-
6 -
Our task can be restated as follows: while the general message emanating
from Module
propagates,
I
it
desired that another module, upon receiving
is
the general message, be able to emit a response message such that when this
is
routed by successively adjoining modules a response message will get to
Module
I.
Routing rules are to be applied local
by each module and in-
1
dependently of others and without site information.
Let us more graphically show that there
ceeding to
solution.
a
Modules
1
c,
wi
1
d,
a
problem here before pro-
Consider Figure 2.
Arrows show the direction of channels.
of Time
is
The general message, at the end
reach modules a and b and at the end of Time 2 will
1
reach
e and f.
Since an addressing scheme
not used. Module a has no way of knowing
is
that the general message came from Module
come from Module
g
or even
f.
I.
For all
Not knowing the source,
it
if
it
wouldn't know, therefore, where to send its response.
It
knew the source to be Module
I,
source since the connecting channel
it
I,
it
might have
it
wanted to respond,
Even assuming that
could not send Its response to this
is
one-way towards Module
the response must be sent to either Module c or
being directly connected to
knows,
but more
d.
Therefore,
a.
However, c or
d
again not
importantly not knowing where
would again be unable to relay the response to
I.
I
is
The problem, therefore,
is
to find some routing rules which, although used locally and independently, will
allow
a
collectivity of modules forming
a
path to bring the response to the
source.
Before the response routing rules the general message propagation rules
must be identified.
a
As the previous discussion also indicates,
general message a module sends
circular paths
a
it
out on al
upon receiving
out-going channels.
general message would never die out.
Due to
Hence, the need for a
-
stopping rule.
We therefore
impose:
-
7
general message having been received
a
once will be ignored upon subsequent arrivals."
Figure 2 the propagation of a general message based on the above rules
In
has been shown.
Heavy elliptic dots mari< the first arrival of the general
message; subsequent arrivals have not been shown, since they are to be
Note that some modules such as
ignored.
in
ill
Figure 2 receive the general
message simultaneously on two channels.
Defining unit time as the time
to a neighboring one
it
takes a message to go from one module
including processing time, we can study the number of
modules reached by the general message as
a
function of time.
Referring to Figure 2 we see that in Time
In
Time
2
four additional modules are covered.
enumeration that for
t>^
it
I
two modules have been reached.
It
can easily be shown by
is:
2
tpr
where
t
is
=»
total
number of modules covered = 2t
-
2t +
1
time that has elapsed since the initiation of the general message.
Our assertion
is
message first arrived
that only remembering the channels on which the general
is
all
that
is
needed for routing
in
the Square Class
C
Selcuk Network.
Let the channels of a Class C Module be
labeled as
when going clockwise, the first input channel will be
in
i
,
Figure
1.
the second
That
i
is
and
similarly for the output channels.
'•'Second
arrivals are important for adaptation to local malfunctions since
failure to receive the second arrival of a G.M. would be indicative of failures
of neighbors and such information can be used to use
routing rules.
a
different set of response
- 8
The response routing rules then are the following:
General Message
First Arrival Channels
Response Route
'2
i
For example,
I
it
comes
is
The proof
It
if
and i^
the GM had first come on
then the response when and
,
no matter what channel
to be sent on
by construction
is
i
In
.
Figure
2
consider Modules
II
can be easily seen that the application of the above rules will
routing rules to all
the modules
in
we allow the channels to be bid rect ional
i
a
GM becomes 2t
2
for all
unidirectional Square Class
C
ponse follows the shortest path.
response time in
a
network.
Call
In
a
the total
,
For large
t.
I.
t
this the shortest
is
also the propagation
response time
.
Actual
Selcuk Network of one-way channels equals the number of
difference between these two response times.
is
nine whereas actual
is
Delay
is
defined as the
For instance for Module
eleven giving
Figure 2 note the spiralling of response paths only
source module.
this
number of modules
bidirectional network the res-
modules, along the path actually taken by response.
est response time
route the
the network shows a definite pattern as
vergence of response paths upon the source, Module
covered by
III.
the examination of wfilch pictorial ly shows the con-
indicated by heavy lines
If
and
Application of the response
response messages as indicated by dotted lines.
in
the response arrived on.
in
a
II
short-
delay of two.
the vicini ty of the
Elsewhere the response paths are straight.
The response
In
delays must, therefore, be independent of the size of the network.
the maximum delay
is
10,
minimum
fact
In
and the approximate average delays for the
four quadrants starting with upper right and going cloci<wise are 0.5, 8.5, ^.5,
2.5, or an overall
this delay
When dealing with thousands of units
of course negligible.
is
Clearly
average delay of 4.
the case of Square Class
in
that are strictly based on local
Network three simple routing rules
C
information and applied independently suffice
for a response from any module to reach the source of a GM.
tion
is
entirely immaterial.
Location informa-
Furthermore nothing would be gained by making
channels two-way since propagation and response times would remain about the
networks would require much more memory
However, two-way channel
same.
The efficiency of the one-way channel
and logic.
Hexagonal
Figure
shows a Hexagonal
3
Note that:
in
on two channels;
is
obvious.
Class K Network
Class K Network and the propagation of a GM,
except
input and output channels alternate;
the Class K Module
along the principal axes
network
(with respect to GM source)
the GM arrives
s
imul
channels
region defined by two adjacent axes the arrival
in a
taneously
remain the same; and if we connect modules that receive the GM at the same time
Counting the modules along triangular propa-
we obtain concentric triangles.
gation fronts we see that the total number of modules covered
is
3/2 t(t+l)
or
2
for large
t
3/2t
Surprisingly despite
.
propagation speed
is
-~>>o,
;
i
and
Class K Modules
i
—^o
is
.
i
so symmetric:
2)
in
the number of channels
-r'O
;
i„-=iO
;
i
—s-o
;
i.
and
i
--70
;
i.
and
The rules can be summarized by two statements since the
channel, the response when and if
output channel and
50% increase
down by about 30%.
Response routing rules are:
i
a
If
1)
it
If
the GM had first arrived on
comes
is
a
single
to be routed on the right adjacent
the GM had arrived simultaneously on two channels then
-
the response
10 -
to be routed on the output channel
is
channels that had carried the GM
Figure
3
shows the application of the
Note the stepstone behavior of response paths at
rules to three modules.
the principal axes.
in.
between the two input
As to be expected from this zigzagging
increases with the size of the network.
Hexagonal Class K not only
is
slower
in
response delay
So compared to Square Class
propagation but also
in
the
C,
response
routing despite a 50% increase in channels and the resultant increase in the
rules, memory, and logic.
to be blamed?
Is
Is
the alternation of input and output channels
More evidence
making input channels adjacent important?
(input channels alternate
can come by examining networks of Square Class D
with output channels) and of Hexagonal Class
input channels).
(adjacent
D
We
will summarize the behavior of these two networks.
Square Class
In
D
the network constructed with Square Class
modules
D
channels alternate with output channels we observed that
a)
which input
in
the total
number
2
of modules covered by the GM
slowest network so far,
b)
is
t(t+l) or for large
response routing
network.
response delays are very much
c)
On all
counts this
is
The Hexagonal Class D module has all
in all
regions
both class
D
is
D
modules
not achievable.
is
if
in
clearly the
,
if one
takes
into
addition to GM arrival
function of the size of the
a
D
input channels adjacent.
constructed
it
and class K modules, making class
D
D
per class
However,
turns out that connectivity
Consequently we constructed
result was a network with three class
network
t
an inferior network.
Hexagonal Class
when a network of Class
only
possible only
is
account the channel on which the response arrives
channels and
t
a
network using
as numerous as possible.
K.
In
one lets a class K type module Initiate the GM
The
this hybrid hexagonal
a)
the total
number
of modules covered rapidly approaches 3n^+3n, the fastest so far and
to propagation
in a
two-way channel hexagonal network
b)
increase with the size of the network and the average
a time unit,
equal
response routing rules
that strictly depend on how the GM had arrived exist and c)
do not
is
response delays
is
about 3/8 of
very negligible.
Clearly making input channels adjacent has dramatically increased efficiency.
Even making the channels two-way will not increase speed but will appreciably
increase the complexity and the logic and memory requirements.
Concl us ions
We have shown that
while
a
in
networks properly constructed with one-way channels,
general message (GM)
propagating
is
a
recipient module can generate
a
response which when routed in accordance with rules that depend strictly on
local
information, will get to the source of the GM,
nor the GM source need know where each other
is
Neither the respondent
located
.
ted by any module and any module can be the respondent.
The GM can be
initia-
Furthermore some
Selcuk Networks of one-way channels rapidly approach the efficiency of two-way
channel
In
networks with approximately half the memory and logic requirements.
the efficient Selcuk Networks
path.
responses follow approximately the shortest
The channel arrangement appears to have a profound impact.
Making input
channels adjacent dramatically improves performance.
The salient features of Selcuk Networks are the following:
routing not only
is
a)
Response
achieved without location-based addressing but also does
not require a central
switchboard;
b)
consequently
if the
network were sectioned
and each section successively removed the remaining sections would operate as
a
processing network and
of the removed sections;
in time
c)
if
can conceivably take over the specialization
there
is
local
failure, second and subsequent
arrivals of the GM can be used to modify routing rules so as to bypass the
-
failed units;
d)
a
12
-
GM can be a string of operations and its propagation can
initiate local processes the results of which can then be collected as "res-
ponses" to the GM source which can be any site
in
the network.
summation or an integration process;
e)
some collection of the modules
this
is
a
through response routing, can form
a
In
some sense
sub-networi< such that after the
initial
propagation of a GM the respondent modules and the source can communicate
among themselves along directed pathways
gonal
.
This has been shown for the Hexa-
Class K Network although the results are not reported here.
Note that
such task partitioning of the network would allow for plasticity as well as
specificity;
f)
finally
in due
time the desired response routes can be made
permanent allowing the taskwise defined subnetwork to remain permanently
connected and specialized
in that
task yet at the same time remaining
of the total network and interacting with
a
part
it.
Such features would seem to make Selcuk Networks potent for content-based
retrieval
in
large arrays,
for parallel
processing machines, for large communi-
cation networks including computer nets and also for pattern recognition
(
25)-
Figure Titles
Figure
1.
Figure 2.
Admissable channel arrangements.
General message propagation and response routing in
Square Class
Figure
3.
C
Selcuk Network.
General message propagation and response routing in
Hexagonal
Class K Selcuk Network.
O2
0;
A
\y
\/
»
V
O3
I
SQUARE
CLASS C
SQUARE
CLASS D
HEXAGONAL
CLASS D
0'
'2
V^
03
HEXAGONAL
HEXAGONAi
CLASS
CLASS
r
^
I
sj^-'^r^
K
RM
ROUTE
GM
L
I
Qu^
J^
h
I
qt>v^
P
Sahin, Ph.D., Member, IEEE
Associate Professor
University of Massachusetts
01002
Amherst, Massachusetts
Kenan
E.
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D,
I
(2)
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.
,
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.
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{k)
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W.J,
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,
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.
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.
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aj_.
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,
,
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