Ger' eb-Graus, M. and Tsantilas, T. 1992. Efficient optical communication in parallel computers. In Proc. ACM Symposium on Parallel Algorithms and Architectures (1992), pp. 41--48.  Home/Search   Document Not in Database   Summary   ACM   TOC   Related Articles   Check

....in which messages arrive according to a probability distribution. Other work [MacKenzie et al. 1998] has focussed on the static scenario in which a given set of users start with messages to send. Similar static contention resolution problems arise in optical routing [Anderson and Miller 1988; Ger eb Graus and Tsantilas 1992; Goldberg et al. 1997] and in simulating shared memory computers on distributed networks [Dietzfelbinger and Meyer auf der Heide 1993; Goldberg et al. 1999; MacKenzie et al. 1998] 1.2 Previous work There has been a tremendous amount of work on protocols for multiple access channels. Here we ....

Ger' eb-Graus, M. and Tsantilas, T. 1992. Efficient optical communication in parallel computers. In Proc. ACM Symposium on Parallel Algorithms and Architectures (1992), pp. 41--48.

....succeed and are acknowledged. The c collision and c arbitrary crossbar models have been studied previously under different names. Our terminology is new. The local memory PRAM model of Anderson and Miller [4] later studied under the name OCPC (optical communication parallel computer) in [7, 8, 9], corresponds to the 1 collision crossbar model. Valiant s S PRAM model [20] corresponds to the 1arbitrary crossbar model. Assuming a complete interconnection between processors and memory modules, the c collision (resp. c arbitrary) DMM models of [6] corresponds to the c collision (resp. ....

....and each memory module is the destination of at most h packets. Thus, a variety of authors have considered the complexity of h relation routing on the 1 collision crossbar. We are particularly interested in a natural randomized h relation routing algorithm proposed by Ger eb Graus and Tsantilas [7]. The idea of their algorithm is to use randomization to break the symmetry between sets of processors with packets to be sent to the same same memory module: In a given round a processor with p packets left to send attempts to send a randomly chosen packet with probability roughly p=h, and does ....

[Article contains additional citation context not shown here]

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, June 1992.

....acknowledged. The c collision and c arbitrary crossbar models have been studied previously under different names. Our terminology is new. The local memory PRAM model of Anderson and Miller [Anderson and Miller 1988] later studied under the name OCPC (optical communication parallel computer) in [Ger eb Graus and Tsantilas 1992; Goldberg and Jerrum 1992; Goldberg et al. 1993] corresponds to the 1 collision crossbar model. Valiant s S PRAM model [Valiant 1990] corresponds On Contention Resolution Protocols and Associated Probabilistic Phenomena Delta 3 to the 1 arbitrary crossbar model. Assuming a complete ....

....and each memory module is the destination of at most h packets. Thus, a variety of authors have considered the complexity of h relation routing on the 1 collision crossbar. We are particularly interested in a natural randomized h relation routing algorithm employed by Ger eb Graus and Tsantilas [Ger eb Graus and Tsantilas 1992]. This algorithm is essentially the same as a previous algorithm proposed by Greenberg and Leiserson [Greenberg and Leiserson 1985] for routing on a fat tree network. The idea of this algorithm is to use randomization to break the symmetry between sets of processors with packets to be sent to ....

[Article contains additional citation context not shown here]

Ger' eb-Graus, M. and Tsantilas, T. 1992. Efficient optical communication in parallel computers. In Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures (June 1992), pp. 41--48.

....resource allocation problems have arisen again, in the context of PRAM emulation (running PRAM algorithms on more realistic models of parallel computation) and in message routing in optical computers. These parallel models include optical networks (Anderson Miller [4] Ger eb Graus Tsantilas [7], Goldberg, Jerrum, Leighton Rao [8] DMM models (Dietzfelbinger Meyer auf der Heide [6] and Valiant s S PRAM model [20] see MacKenzie, Plaxton Rajaraman [14] for details. In addition, MACs provide a good model to study the abstract problem of distributed contention resolution for a ....

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proc. ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, 1992.

....modules. In this case, a processor that wants to access module M directs a beam of light to the receptor (which corresponds to the communication window) of M . Only if M gets at most a small number of messages, it can identify and process them. For earlier work on 1 collision DMMs see, e.g. [1, 8, 24, 25]) We omit the details of writing to or reading from the representations of the memory cells in the modules Mk , and just focus on the property of the DMM that access is granted to up to c processors requesting access. If space efficiency within the modules is not an issue, each module can keep ....

....which come close to this ideal. ffl simplicity: We strive for very simple simulations, i.e. very simple access schedules. This is not a formal measure. e.g. we try to find schedules which are deterministic (except for the random choice of hash functions) and that are pure in the sense of [8], i.e. the only kind of communication that takes place between processors and memory modules is that processors try to pass access requests to the modules addressed by these requests; no key distribution or other calculations take place. 1.3 Previously known results about PRAM simulations on ....

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M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proc. of the 4th Ann. ACM Symp. on Parallel Algorithms and Architectures, pp. 41--48, 1992.

....for the multi hop radio networks are often required to be robust enough to run in ad hoc networks. We assume that the multi hop radio networks are ad hoc, when considering distributed protocols, unless stated otherwise. A model related to radio networks is that of optical communication (see [38, 41, 42]) To explain the relationship, notice that a radio network can be interpreted as operating under just one wave frequency used by all the nodes. The term optical communication is usually employed when Randomized Communication in Radio Networks 5 many frequencies are used simultaneously, up to as ....

.... the all broadcast problem for the multiple access channel, when each of some k among the n stations needs to broadcast its message on the optical channel, and each of the stations with messages does know the number k, has been called the control tower problem in [64] Ger eb Graus and Tsantilas [38] developed a randomized protocol solving this problem in time O(k lg n lg k) with the probability polynomially close to one. MacKenzie, Plaxton and Rajaraman [64] proved the following lower bound: if a randomized algorithm solving the control tower problem operates in time T (n; k) with ....

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M. Ger'eb-Graus, and T. Tsantilas, Efficient optical communication in parallel computers, in Proc. 4th Ann. ACM Symp. on Parallel Algorithms and Architectures, 1992, pp. 41--4.

....some models that have been studied previously. The module parallel computer (MPC [9] and the S PRAM [116] correspond to the 1 arbitrary crossbar model. The local memory PRAM model of Anderson and Miller [10] later studied under the name OCPC (optical communication parallel computer) in [51, 60, 61], corresponds to the 1 collision crossbar model. The c arbitrary and c collision DMM models of [47, 75] are similar to the crossbar models in that the underlying communication network is a complete network. The DMM models, however, limit only the total number of objects accessed from a node to c ....

....of replication, a natural approach to resolve contention for MACs is to use randomization to break the symmetry among the clients. This idea is central to many MAC protocols, including the Ethernet protocol [92] and the slotted ALOHA 20 protocol [1] and routing protocols for the optical computer [10, 116, 51]. For more work in this direction, see [64, 65] Lower bounds for routing in optical computers appear in [62, 88] 2.2 The 1 out of Protocol Consider the 1 out of problem where 1. Let the hash functions be labeled h i , 0 i , and the shared memory request of node j be for cell ....

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, June 1992.

....component can transmit a message to any other, but only those receive messages that have just one targeted at them in that cycle. The senders find out immediately whether their transmission succeeded. Known general simulations of the BSP on the S PRAM with slack log p or slightly more are known [3], 15] and these imply constant factor optimal implementations of our combining algorithm on the S PRAM. There are clearly several possibilities for more efficient direct implementations also. So far we have discussed versions of the algorithm that implement (q,r) patterns in a hashed address ....

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. Proc. 4th ACM Symp. on Parallel Algorithms and Architectures, June 29-July 1, (1992) 41-48.

....on a wavelength and P j listens to the same wavelength. One may view the abstract pos model as a generalization of the Optical Communication Parallel Computer ocpc. This model, introduced by Anderson and Miller [AM88] has recently attracted increased attention of the theoretical community [GT92, GV94, Rao92, GJLR93, GMR94, GJM94] Whereas the pos model is described in terms of light moving in fibers, the ocpc model is better described in terms of light beams moving in free space. Similar to the pos, an n processor ocpc is composed of n processors, each having a transmitter and a ....

M. Ger'eb-Grauss and T. Tsantilas. Efficient optical communication in parallel computers. In ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, June 1992.

....support an important number of elements, restrictions, such as limitations on the number of available wavelengths and bounded number of receivers of a single message, are considered. The completely connected Optical Communication Parallel Computer (OCPC) can be seen as particular case of our model[17 20]. The OCPC has become quite popular in the last few years, because of its relation to a specific model of PRAM: the ERCW PRAM[21] Details on both models are given in Section 2. These restrictive assumptions, motivated by implementation issues of optical components, make simple communication ....

....by a receiver to stop receiving on a given wavelength when it is tuning to another one. Clearly, ffi ae r . When ffi = 0, we say that detuning is instantaneous . 2. 2 Optical Communication Parallel Computer A highly theoretical model known as the OCPC (for Optical Communication Parallel Computer)[17 19] has received considerable attention lately. It can be seen as N elementary processors with a local memory, whose nodes are connected by a complete graph and can communicate with any other node (one to one communications) in a single hop. In this model, the transmitters are tunable, but the ....

M. Ger'eb-Grauss and T. Tsantilas. Efficient optical communication in parallel computers. In ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, June 1992.

....is an example of the distributed memory model. It consists of a collection of processors and a collection of memory modules (Anderson and Miller 1988) Each memory module is connected to one processor. Processors communicate with each other by transmitting messages (Anderson and Miller 1988, Ger b Graus and Tsantilas 1992, Goldberg al. 1993) A processor can transmit a message to any other processor and the transmission takes a constant time. At any time a processor can send at most one message. The message will succeed in reaching the processor if it is the only message with that processor as its destination ....

....PRAM model has shared memory and it is therefore more comfortable to program. There are many studies about simulation of SMM on DMM in different interconnection networks, such as mesh (Leighton 1992) butterfly (Ranade 1991) hypercube (Valiant 1990) complete network (Anderson and Miller 1988, Ger b Graus and Tsantilas 1992, Goldberg al. 1993, Goldberg al. 1994, Karp al. 1992) and MOB (Goldberg al. 1993) The simulation of DMM has two components: Address map. Mapping the address space of the PRAM onto the N memory modules of the network, so that the PRAM consists of processors P 1 ,P 2 , P p and shared ....

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Geréb-Graus M., Tsantilas T.1992: Efficient Optical Communication in Parallel Computers.

....the best (asymptotically smallest delay) time processor optimal simulation of a P log log P processor EREW with delay log log P . Their simulation is rather complicated and therefore it is probably difficult to realize in practice. A more practical approach is taken by Ger eb Graus and Tsantilas [2] who study direct h relation realization algorithms using only one hash function. An h relation realization algorithm is direct, if it sends only original messages and only to the original targets. In [2] Ger eb Graus and Tsantilas present so far the best direct h relation realization ....

....to realize in practice. A more practical approach is taken by Ger eb Graus and Tsantilas [2] who study direct h relation realization algorithms using only one hash function. An h relation realization algorithm is direct, if it sends only original messages and only to the original targets. In [2], Ger eb Graus and Tsantilas present so far the best direct h relation realization algorithm, which works in time O(h log P log log P ) 2 A. Kautonen, V. Leppanen and M. Penttonen Their algorithm yields a time processor optimal EREW simulation for h = Omega (log P log log P ) with high ....

M. Ger'eb-Graus and T. Tsantilas. Efficient Optical Communication in Parallel Computers. In SPAA'92, 4th Annual Symposium on Parallel Algorithms and Architectures, San Diego, California, pages 41 -- 48, June 1992.

....succeed and are acknowledged. The c collision and c arbitrary crossbar models have been studied previously under different names. Our terminology is new. The local memory PRAM model of Anderson and Miller [5] later studied under the name OCPC (optical communication parallel computer) in [10, 11, 12], corresponds to the 1 collision crossbar model. Valiant s S PRAM model [25] corresponds to the 1 arbitrary crossbar model. Assuming a complete interconnection between processors and memory modules, the c collision (resp. c arbitrary) DMM models of [9] corresponds to the c collision (resp. ....

....and each memory module is the destination of at most h packets. Thus, a variety of authors have considered the complexity of h relation routing on the 1 collision crossbar. We are particularly interested in a natural randomized h relation routing algorithm employed by Ger eb Graus and Tsantilas [10]. This algorithm is essentially the same as a previous algorithm proposed by Greenberg and Leiserson [16] for routing on a fat tree network. The idea of this algorithm is to use randomization to break the symmetry between sets of processors with packets to be sent to the same memory module: In a ....

[Article contains additional citation context not shown here]

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, June 1992.

....and two receivers, only one of each being tunable. One may view the abstract pos model as a generalization of the Optical Communication Parallel Computer ocpc. This model, introduced by Anderson and Miller [AM88] has recently attracted increased attention of the theoretical community [GT92, GV94, Rao92, GJLR93, GMR94, GJM94] Whereas the pos model is described in terms of light moving in fibers, the ocpc model is better described in terms of light beams moving in free space. Similar to the pos, an n processors ocpc is composed of n processors, each having a transmitter and a ....

M. Ger'eb-Grauss and T. Tsantilas. Efficient optical communication in parallel computers. In 4-th ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, June 1992.

....consider the construction and evaluation of the hash functions used in our simulation algorithm. 1. 1 Related work The OCPC model The ocpc model was first introduced by Anderson and Miller [2] and Eshaghian and Kumar [10] and has been studied by Valiant [40] Ger eb Graus and Tsantilas [12], Gerbessiotis and Valiant [11] Rao [33] Goldberg, Jerrum, Leighton and Rao [17] and Goldberg, Jerrum and MacKenzie [18] The feasibility of the ocpc from an engineering point of view is discussed in [2, 12] See also the survey paper of McColl [30] and the references therein. Computing ....

.... Eshaghian and Kumar [10] and has been studied by Valiant [40] Ger eb Graus and Tsantilas [12] Gerbessiotis and Valiant [11] Rao [33] Goldberg, Jerrum, Leighton and Rao [17] and Goldberg, Jerrum and MacKenzie [18] The feasibility of the ocpc from an engineering point of view is discussed in [2, 12]. See also the survey paper of McColl [30] and the references therein. Computing h relation on the OCPC A fundamental problem that deals with contention resolution on the ocpc is that of realizing an h relation. In this problem, each processor has at most h messages to send and at most h messages ....

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M. Ger'eb-Graus and T. Tsantilas, Efficient Optical Communication in Parallel Computers, Proceedings of the ACM Symposium On Parallel Algorithms and Architectures 4 (1992) 41--48.

....explicitly consider the construction and evaluation of the hash functions used in our simulation algorithm. 1. 1 Related work The OCPC model The ocpc model was first introduced by Anderson and Miller [2] and Eshaghian and Kumar [10] and has been studied by Valiant [39] Ger eb Graus and Tsantilas [12], Gerbessiotis and Valiant [11] Rao [33] Goldberg, Jerrum, Leighton and Rao [17] and Goldberg, Jerrum and MacKenzie [18] The feasibility of the ocpc from an engineering point of view is discussed in [2, 12] See also the survey paper of McColl [30] and the references therein. Computing ....

.... Eshaghian and Kumar [10] and has been studied by Valiant [39] Ger eb Graus and Tsantilas [12] Gerbessiotis and Valiant [11] Rao [33] Goldberg, Jerrum, Leighton and Rao [17] and Goldberg, Jerrum and MacKenzie [18] The feasibility of the ocpc from an engineering point of view is discussed in [2, 12]. See also the survey paper of McColl [30] and the references therein. Computing h relation on the OCPC A fundamental problem that deals with contention resolution on the ocpc is that of realizing an h relation. In this problem, each processor has at most h messages to send and at most h messages ....

[Article contains additional citation context not shown here]

M. Ger'eb-Graus and T. Tsantilas, Efficient Optical Communication in Parallel Computers, Proceedings of the ACM Symposium On Parallel Algorithms and Architectures 4 (1992) 41--48.

....on dynamically reconfigurable optical networks. Specifically, we show that the ERCW PRAM (using the Tolerant protocol for resolving write conflicts) with n global memory cells and unlimited local memory is computationally equivalent to the OCPC (Optical Communication Parallel Computer) model [1, 21, 22, 24, 43] on n processors. This is in contrast to the statement given in [1] that the OCPC model is equivalent to an EREW PRAM with n global memory cells. Since the OCPC model uses full dynamic reconfiguration which is not yet technically feasible, we are interested in developing oblivious ERCW PRAM ....

....it is still not as fast as an electronic switch. 8. 2 OCPC model One abstraction of the beam steering model (which could also be considered an abstraction of the passive optical star coupler with tunable transmitters) was first considered by Anderson and Miller [1] and has since been studied in [12, 15, 21, 22, 24, 25, 37, 43]. Various names for this model have been proposed, including Local Memory PRAM, S PRAM, OMC, OCP, and OCPC. We will use the term OCPC, denoting Optical Communication Parallel Computer. An OCPC consists of a collection of processors, each with infinite local memory, which operate synchronously and ....

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proc. ACM Symp. on Para. Alg. and Arch., pages 41--48, 1992.

....restrictions results in a run time computation error. Another model attracting growing interest is the Optical Communication Parallel Computer (OCPC) also called Distributed Memory Machine [16] Direct Connection Machine [13] or S PRAM [20] It models a completely connected optical network (see [1, 4, 6, 15, 18]) All processors have their local control and memory modules attached. Every processor A can attempt to communicate directly with any processor B in a unit of time. If at the moment of communication A is the only processor attempting to communicate with B, then the communication is successful. ....

M. Ger'eb-Graus and T. Tsantilas, Efficient optical communication in parallel computers, in Proceedings of the 4th Ann. ACM Symposium on Parallel Algorithms and Architectures, 1992, pp. 41--48.

....or h relations [27] 2.3 Previous Results and Extensions In [20] the AROB model has been defined. Similar models have been employed before as well (see e.g. 19] A related model known as the Optical Communication Parallel Computer (OCPC) has also been defined in the literature (see e.g. 1] [8], 27] 9] In an OCPC any processor can communicate with any other processor in one unit of time, provided there are no conflicts. If more than one processors try to send a message to the same processor, no message reaches the intended destination. In [20] algorithms for such problems as ....

....runs on the AROB preserving the run time. Routing on the OCPC. Several packet routing algorithms for the OCPC model can be found in the literature. Anderson and Miller have shown that a special case of log n relations on an n node OCPC can be routed in e O(log n) time [1] Also, 27] and [8] have presented efficient algorithms for h relations. An algorithm for arbitrary h relations with a run time of e O(h log log n) has been given by Goldberg, Jerrum, Leighton, and Rao [9] 2.4 New Results In this paper we present a sorting algorithm that can sort n general keys in O(1) time on ....

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M. Ger'eb-Graus and T. Tsantilas, Efficient Optical Communication in Parallel Computers, Symposium on Parallel Algorithms and Architectures, 1992, pp. 41-48.

....hardware and the work complexity of the routing machinery components. Some of the simulations results are recently surveyed in [6] see also [22] 1.1. 1 Ignoring restrictions of physical space The implementation of the PRAM models on completely connected networks has been studied e.g. in papers [41, 49, 3, 5, 30, 51, 27, 19, 12, 10, 20, 52, 22]. In [51] Valiant showed how a P processor RCN (Rejecting Complete Network: the memory module of a processor accepts at most one memory request at a given step; informs about rejection in constant time) can simulate EREW (P log P ) and weaker) PRAM models work optimally with high probability. ....

M. Ger'eb-Graus and T. Tsantilas. Efficient Optical Communication in Parallel Computers. In SPAA'92, 4th Annual Symposium on Parallel Algorithms and Architectures, San Diego, California, pages 41 -- 48, June 1992.

....all requests arriving at one module are processed in one step, as long as there are at most c of them; otherwise none is processed. An answer is only accessible by the issuing processor. Note : For c = 1 this model corresponds to a communication mechanism based on optical crossbars (compare [1] [9] and [22] c collision DMMs can easily be simulated on arbitrary DMMs with delay O(c) Randomized versions of the above models are obtained by adding the capability of choosing a random integer from a finite range. 1.2 Dictionaries and Shared Memory Simulations Shared memory simulations on a ....

M. Ger'eb-Graus and T. Tsantilas, Efficient optical communication in parallel computers, in: Proc. SPAA'92, 41-48.

.... the use of randomness is fundamental; to our knowledge, the best upper bound for deterministically routing an arbitrary h relation on an OCPC is O(h log n) The direct algorithm with the best asymptotic running time for the OCPC is the simple randomized algorithm of Gereb Graus and Tsantilas [GT 92] For any fixed ffl 0, their algorithm with high probability transmits an arbitrary h relation in time e 1 Gamma ffl h Theta( p h log n log n log log n) This is done with log 1= 1 Gammaffl) h = log h Gamma log(1 Gammaffl) phases, where the problem remaining at the start of phase i ....

....of a message can be acknowledged in unit time; those processors which do not receive an acknowledgment can assume their messages were not transmitted successfully. The algorithm we employ is similar to the direct algorithm for routing h relations on the OCPC due to Ger ebGraus and Tsantilas [GT 92] By continuously updating weighted transmission probabilities for messages from sender i to receiver j, we obtain an algorithm which routes h relations in the arbitrary write model with a small leading constant. We work toward the proof of the following theorem, which gives us a bound on routing ....

[Article contains additional citation context not shown here]

M. Ger'eb-Graus and T. Tsantilas. "Efficient Optical Communication in Parallel Computers," Proc. 4th ACM Symp. on Parallel Algorithms and Architectures, pp. 41-48, June 1992.

....Research Projects Grants 003658480 and 003658386, and NSF Grant CCR 90 23059. vlr cs.utexas.edu) the Tolerant protocol for resolving write conflicts) with n global memory cells and unlimited local memory is computationally equivalent to the OCPC (Optical Communication Parallel Computer) model [3, 28, 29, 31, 50] on n processors. This is in contrast to the statement given in [3] that the OCPC model is equivalent to an EREW PRAM with n global memory cells. In previous work, it was shown that the EREW PRAM could be simulated on the OCPC with some overhead per step [44, 18] This overhead was a result of ....

....it is still not as fast as an electronic switch. 3. 2 OCPC model One abstraction of the beam steering model (which could also be considered an abstraction of the passive optical star coupler with tunable transmitters) was first considered by Anderson and Miller [3] and has since been studied in [18, 22, 28, 29, 31, 32, 44, 50]. Various names for this model have been proposed, including Local Memory PRAM, S PRAM, OMC, OCP, and OCPC. We will use the term OCPC, denoting Optical Communication Parallel Computer. An OCPC consists of a collection of processors, each with infinite local memory, which operate synchronously and ....

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proc. ACM Symp. on Para. Alg. and Arch., pages 41--48, 1992.

....and it does not receive any of the messages. The OCPC was first introduced as a model of computation by Anderson and Miller [AM 88] who called this model the Local Memory PRAM. Since then it has been studied by Valiant [Val 90] who called the model the S PRAM) by Ger eb Graus and Tsantilas [GT 92] and by Gerbessiotis and Valiant [GV 92] who also called the model the S PRAM) The feasibility of the OCPC from a engineering point of view is discussed in [AM 88, GT 92, and Rao 92] See also the references in [McC 92] In the first part of this paper we study the problem of interprocessor ....

.... Since then it has been studied by Valiant [Val 90] who called the model the S PRAM) by Ger eb Graus and Tsantilas [GT 92] and by Gerbessiotis and Valiant [GV 92] who also called the model the S PRAM) The feasibility of the OCPC from a engineering point of view is discussed in [AM 88, GT 92, and Rao 92] See also the references in [McC 92] In the first part of this paper we study the problem of interprocessor communication on an OCPC. In particular, we study the problem of realizing h relations. An h relation (see [Val 90] is a communication problem in which each processor has up ....

[Article contains additional citation context not shown here]

M. Ger'eb-Graus and T. Tsantilas, Efficient Optical Communication in Parallel Computers, Proceedings of the ACM Symposium On Parallel Algorithms and Architectures 4 (1992) 41--48.

....succeed and are acknowledged. The c collision and c arbitrary crossbar models have been studied previously under different names. Our terminology is new. The local memory PRAM model of Anderson and Miller [5] later studied under the name OCPC (optical communication parallel computer) in [10, 11, 12], corresponds to the 1 collision crossbar model. Valiant s S PRAM model [24] corresponds to the 1 arbitrary crossbar model. Assuming a complete interconnection between processors and memory modules, the c collision (resp. c arbitrary) DMM models of [9] corresponds to the c collision (resp. ....

....and each memory module is the destination of at most h packets. Thus, a variety of authors have considered the complexity of h relation routing on the 1 collision crossbar. We are particularly interested in a natural randomized h relation routing algorithm proposed by Ger eb Graus and Tsantilas [10]. The idea of their algorithm is to use randomization to break the symmetry between sets of processors with packets to be sent to the same same memory module: In a given round a processor with p packets left to send attempts to send a randomly chosen packet with probability roughly p=h, and does ....

[Article contains additional citation context not shown here]

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, June 1992.

....focus on the dynamic contention resolution problem in which messages arrive according to a probability distribution. Other work [17] has focussed on the static scenario in which a given set of users start with messages to send. Similar static contention resolution problems arise in optical routing [4, 8, 9] and in simulating shared memory computers on distributed networks [7, 10, 17] 1.2 Previous work There has been a tremendous amount of work on protocols for multiple access channels. Here we will only discuss theoretical results concerning dynamic protocols in the acknowledgment based model ....

M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proc. ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, 1992.

....transmission is detected by the absence of such an acknowledgement message. Thus, in constant time, all the processors requesting accesses are informed whether they have succeeded. A very simple randomized protocol for routing h relations on an N OCPC is described by Ger eb Graus and Tsantilas in [8]. Their protocol runs in time Theta(h log N log log N ) A much more complicated protocol that runs in time Theta(h log log N ) is described in [10] For either protocol, however, the constant factor is about 5.5. In contrast, for large h, our total exchange based protocols achieve 1optimality ....

M. Ger' eb-Graus and T. Tsantilas, Efficient optical communication in parallel computers, in 4th Symposium on Parallel Algorithms and Architectures (SPAA '92), 1992.

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M. Ger'eb-Graus and T. Tsantilas. Efficient optical communication in parallel computers. In Proceedings of the 4th Annual ACM Symposium on Parallel Algorithms and Architectures, pages 41--48, June 1992.

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