Abstract not found

We study contention resolution problem in a multiple-access channel such as the Ethernet...

... programs using high-level, general-purpose, and architecture-independent programming language and have them executedonavarietyofparallelanddistributed architectureswithout sacricing efficiency. Alargebodyofresearchsuggeststhat,atleastintheory, general-purposeparallelcomputingisindeedpossibleprovided certainconditionsaremet: anexcessoflogicalparallelismin the program,andtheabilityofthetargetarchitectureto efficientlyrealizebalancedcommunication patterns. Thecanonicalexampleofabalancedcommunicationpatternisan h-relation, inwhicheachprocessoristheorigin and destination of at most h messages. A plethoraofprotocolshasbeendesigned forrouting h-relations inavarietyofnetworks. Thegoalhasbeentominimizethevalueofhwhile guaranteeingdeliveryofthemessageswithintime aconstantfactorfromoptimal.Inthispaperwe describeprotocolsthatmeetthemoststringent efficiency requirement, namely deliveryofmessages withintimethatisalowerorderadditivetermfrom thebestachievable. Suchprotocolsarecalled 1-optimal. Whiletheseprotocolsachieve1-optimality only forheavilyloadednetworks,thatis,for largevaluesofh, theyareremarkablefortheirsimplicityinthattheyonly usethetotal-exchange communication primitive. The total-exchange canberealizedinmanynetworksusingverysimple, contention-free,andextremely efficient schemes. Thetechnicalcontributionofthispaperisaprotocol torouterandomh-relationsinan N-processor networkusing hN(1+o(1))+O(loglogN) total-exchange roundswithhighprobability. Usingmessageduplication, wecanimprovetheboundto hN(1+o(1))+O(logN). This improves upon the hN(1+o(1))+O(logN) bound of Gerbessiotis and Valiant. While our theoretical improvements are modest, our experimental results show an improvement over the protocol of Gerebessiotis and Valiant.

. Optical communication is likely to significantly speed up parallel computation because the vast bandwidth of the optical medium can be divided to produce communication networks of very high degree. However, the problem of contention in high-degree networks makes the routing problem in these networks theoretically (and practically) di#cult. In this paper we examine Valiant's h-relation routing problem, which is a fundamental problem in the theory of parallel computing. The h-relation routing problem arises both in the direct implementation of specific parallel algorithms on distributed-memory machines and in the general simulation of shared-memory models such as the PRAM on distributed-memory machines. In an h-relation routing problem each processor has up to h messages that it wishes to send to other processors and each processor is the destination of at most h messages. We present a lower bound for routing an h-relation (for any h > 1) on a complete optical network of size n. Our lo...