Hawaii International Conference on System Sciences

http://compalg.inf.elte.hu/~tony/Kutatas/BinPacking/Johnson-BinPacking-NP-Column-JAlg-2002.pdf

The NP-completeness column: An ongoing guide

Publisher Summary
This chapter discusses parallel algorithms for shared-memory machines. Parallel computation is rapidly becoming a dominant theme in all areas of computer science and its applications. It is estimated that, within a decade, virtually all developments in computer architecture, systems programming, computer applications and the design of algorithms will be taking place within the context of parallel computation. In preparation for this revolution, theoretical computer scientists have begun to develop a body of theory centered on parallel algorithms and parallel architectures. As there is no consensus yet on the appropriate logical organization of a massively parallel computer, and as the speed of parallel algorithms is constrained as much by limits on interprocessor communication as it is by purely computational issues, it is not surprising that a variety of abstract models of parallel computation have been pursued. Closest to the hardware level are the VLSI models, which focus on the technological limits of today's chips, in which gates and wires are packed into a small number of planar layers.

Parallel algorithms for shared-memory machines

The class NC consists of problems solvable very fast (in time polynomial in log n ) in parallel with a feasible (polynomial) number of processors. Many natural problems in NC are known; in this paper an attempt is made to identify important subclasses of NC and give interesting examples in each subclass. The notion of NC 1 -reducibility is introduced and used throughout (problem R is NC 1 -reducible to problem S if R can be solved with uniform log-depth circuits using oracles for S ). Problems complete with respect to this reducibility are given for many of the subclasses of NC . A general technique, the “parallel greedy algorithm,” is identified and used to show that finding a minimum spanning forest of a graph is reducible to the graph accessibility problem and hence is in NC 2 (solvable by uniform Boolean circuits of depth O (log 2 n ) and polynomial size). The class LOGCFL is given a new characterization in terms of circuit families. The class DET of problems reducible to integer determinants is defined and many examples given. A new problem complete for deterministic polynomial time is given, namely, finding the lexicographically first maximal clique in a graph. This paper is a revised version of S. A. Cook, (1983, in “Proceedings 1983 Intl. Found. Comut. Sci. Conf.,” Lecture Notes in Computer Science Vol. 158, pp. 78–93, Springer-Verlag, Berlin/New York).

A taxonomy of problems with fast parallel algorithms

This volume provides an ideal introduction to key topics in parallel computing. With its cogent overview of the essentials of the subject as well as lists of P -complete- and open problems, extensive remarks corresponding to each problem, a thorough index, and extensive references, the book will prove invaluable to programmers stuck on problems that are particularly difficult to parallelize. In providing an up-to-date survey of parallel computing research from 1994, Topics in Parallel Computing will prove invaluable to researchers and professionals with an interest in the super computers of the future.

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Limits to Parallel Computation: P-Completeness Theory

Parallel time is clearly a fundamental complexity resource for synchronous parallel computation. But study of parallel time complexity classes alone does not give complete insight into the cost of a parallel computation: clearly the number of processors and amount of circuitry involved is also important. In this paper we examine the parallel resource hardware, and relate hardware complexity classes to previously studied resource classes. As motivation for studying hardware complexity, observe that while there has developed a substantial body of evidence showing that sequential Turing machine space can be simulated efficiently by parallel time (see [CS] or [GI], where this relationship is called the "parallel computation thesis"), these simulations do not constrain the hardware used by the parallel machine, and in fact use an exponential (in the Tm space) amount of hardware. For example, SAT can be accepted in linear space, thus in linear time on a SIMDAG [GI], but if P ; NP, more than a polynomial amount of hardware will be required to do so.

Hardware complexity and parallel computation

We present a randomized parallel algorithm for constructing the 3D convex hull on a generic p-processor coarse grained multicomputer with arbitrary interconnection network and n/p local memory per processor, where ~ z p’+’ (for some arbitrarily small c > O). For any given set of n points in 3-space, the algorithm computes the 3D convex hull, with high probability, in 0(w) local computation time and 0(1 ) communication phases with at most 0(~) data sent/received by each processor. That is, with high probability, the algorithm computes the 3D convex hull of an arbitrary point set in time 0(* + I’~,P), where I’~,P denotes the time complexity of one communication phase. In the terminology of the BSP model, our algorithm requires, with high probability, O(1) supersteps and a synchronization period @(%). In the LogP model, the execution time of our algorithm is asymptotically optimaJ for several archit ect ures. ● This work was partially supported by the Natural Sciences and Engineering Research Council of Canada and the ESPRIT Basic Research Actions Nr. 7141 (ALCOM II). tschool of Computer Science, Carleton Univer.9ity, Ottawa, Canada KIS 5B6. Email: dehne@scs. carlet on. ca ~J@t. of Computer Science, York University, NOrth York, Canada M3J 1P3. Email: {deng, dyrnond}@cs .yorku. ca 5 Dept. of Computer Science, Utrecht University, 3508 TB Utrecht, The Netherlands. Email: andreas@cs .ruu. nl II School Of EE and Dept. of Computer Sci., Purdue University, West Lafayette, IN 47907, USA. Email: ashf aq~cs .purdue. edu Permission to make. digitirl/llarci copies of :111or p:~rt of [his nl:llcri:ll wiLhout fee is granted provided lhat the ct]pics ;Ire II(J1 m:ldc {Jr dis~l-il,~itcd for profit or commercial advantage, the ACM copyrighl/sccvcr notice, the title of the publication and its date appear, and notice is given that copyright is by permission of the Association for Computin: Machinery, Inc. (ACM). To copy otherwise, to repuhlish,[o post on servers or LO redistribute to lists, requires specific permission and/cor ftx, SPAA’95 Santa Bmlxm CA USA(”) 1995 ACM O-89791 -717-0/9.5/07.S3.50

A randomized parallel 3D convex hull algorithm for coarse grained multicomputers

We show that there is a good algorithm for scheduling the average completion time of a set of unknown DAGs (i.e., data dependency relation graphs of programs) on a multiprocessor in the PRAM model (Karp and Ramachandran, 1990) (orother similar shared memory models.) Then, we show that a large class ofparallel jobs can be scheduled with near-optimal average completion time in the BSP model (Valiant, 1990a) though this is not possible for theclass of all unknown DAGs (Deng and Koutsoupias, 1993) (the same holds forother similar distributed memory models.)

On multiprocessor system scheduling

The parallel pointer machine is a synchronous collection of finite state transducers, each transducer receiving its inputs via pointers to the other transducers. Each transducer may change its input pointers dynamically by “pointer jumping”. These machines provide a simple example of a parallel model with a time-varying processor inter-connection structure, and are sufficiently powerful to simulate deterministic spaceS(n) within timeO(S(n)).

Parallel pointer machines

This paper explores two enhancements that can be made to single and multiple robot exploration in graph-like worlds. One enhancement considers the order in which potential places are explored and another considers the exploitation of local neighbor information to help disambiguate possible locations. Empirical evaluations show that both enhancements can produce a significant reduction in exploration effort in terms of the number of mechanical steps required over the original exploration algorithms and that for some environments up to 60% reduction in mechanical steps can be achieved.

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Patrick W. Dymond

Papers

Hardware complexity and parallel computation

A randomized parallel 3D convex hull algorithm for coarse grained multicomputers

On multiprocessor system scheduling

Parallel pointer machines

Enhancing Exploration in Graph-like Worlds