Results 1  10
of
15
On Chromatic Sums and Distributed Resource Allocation
"... This paper studies an optimization problem that arises in the context of distributed resource allocation: Given a conflict graph that represents the competition of processors over resources, we seek an allocation under which no two jobs with conflicting requirements are executed simultaneously. Our ..."
Abstract

Cited by 66 (14 self)
 Add to MetaCart
This paper studies an optimization problem that arises in the context of distributed resource allocation: Given a conflict graph that represents the competition of processors over resources, we seek an allocation under which no two jobs with conflicting requirements are executed simultaneously. Our objective is to minimize the average response time of the system. In alternative formulation this is known as the Minimum Color Sum (MCS) problem [24]. We show, that the algorithm based on finding iteratively a maximum independent set (MaxIS) is a 4approximation to the MCS. This bound is tight to within a factor of 2. We give improved ratios for the classes of bipartite, boundeddegree, and line graphs. The bound generalizes to a 4aeapproximation of MCS for classes of graphs for which the maximum independent set problem can be approximated within a factor of ae. On the other hand, we show that an n1 \Gamma fflapproximation is NPhard, for some ffl? 0. For some instances of the resource allocation problem, such as the Dining Philosophers, an efficient solution requires edge coloring of the conflict graph. We introduce the Minimum Edge Color Sum (MECS) problem which is shown to be NPhard. We show that a 2approximation to MECS(G) can be obtained distributively using compact coloring within O(log² n) communication rounds.
The Complexity of Computation on the Parallel Random Access Machine
, 1993
"... PRAMs also approximate the situation where communication to and from shared memory is much more expensive than local operations, for example, where each processor is located on a separate chip and access to shared memory is through a combining network. Not surprisingly, abstract PRAMs can be much m ..."
Abstract

Cited by 32 (4 self)
 Add to MetaCart
PRAMs also approximate the situation where communication to and from shared memory is much more expensive than local operations, for example, where each processor is located on a separate chip and access to shared memory is through a combining network. Not surprisingly, abstract PRAMs can be much more powerful than restricted instruction set PRAMs. THEOREM 21.16 Any function of n variables can be computed by an abstract EROW PRAM in O(log n) steps using n= log 2 n processors and n=2 log 2 n shared memory cells. PROOF Each processor begins by reading log 2 n input values and combining them into one large value. The information known by processors are combined in a binarytreelike fashion. In each round, the remaining processors are grouped into pairs. In each pair, one processor communicates the information it knows about the input to the other processor and then leaves the computation. After dlog 2 ne rounds, one processor knows all n input values. Then this processor computes th...
On Parallel Hashing and Integer Sorting
, 1991
"... The problem of sorting n integers from a restricted range [1::m], where m is superpolynomial in n, is considered. An o(n log n) randomized algorithm is given. Our algorithm takes O(n log log m) expected time and O(n) space. (Thus, for m = n polylog(n) we have an O(n log log n) algorithm.) The al ..."
Abstract

Cited by 25 (9 self)
 Add to MetaCart
The problem of sorting n integers from a restricted range [1::m], where m is superpolynomial in n, is considered. An o(n log n) randomized algorithm is given. Our algorithm takes O(n log log m) expected time and O(n) space. (Thus, for m = n polylog(n) we have an O(n log log n) algorithm.) The algorithm is parallelizable. The resulting parallel algorithm achieves optimal speed up. Some features of the algorithm make us believe that it is relevant for practical applications. A result of independent interest is a parallel hashing technique. The expected construction time is logarithmic using an optimal number of processors, and searching for a value takes O(1) time in the worst case. This technique enables drastic reduction of space requirements for the price of using randomness. Applicability of the technique is demonstrated for the parallel sorting algorithm, and for some parallel string matching algorithms. The parallel sorting algorithm is designed for a strong and non standard mo...
Efficient String Algorithmics
, 1992
"... Problems involving strings arise in many areas of computer science and have numerous practical applications. We consider several problems from a theoretical perspective and provide efficient algorithms and lower bounds for these problems in sequential and parallel models of computation. In the sequ ..."
Abstract

Cited by 8 (6 self)
 Add to MetaCart
Problems involving strings arise in many areas of computer science and have numerous practical applications. We consider several problems from a theoretical perspective and provide efficient algorithms and lower bounds for these problems in sequential and parallel models of computation. In the sequential setting, we present new algorithms for the string matching problem improving the previous bounds on the number of comparisons performed by such algorithms. In parallel computation, we present tight algorithms and lower bounds for the string matching problem, for finding the periods of a string, for detecting squares and for finding initial palindromes.
Sigma\Pi\Sigma threshold formulas
 Combinatorica
, 1994
"... A ΣΠΣ formula has the form � � � u v w Luvw, where each L is either a variable or a negated variable. In this paper we study the computation of threshold functions by ΣΠΣ formulas. By combining the proof of the FredmanKomlós bound [5, 10] and a counting argument, we show that for k and n large and ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
A ΣΠΣ formula has the form � � � u v w Luvw, where each L is either a variable or a negated variable. In this paper we study the computation of threshold functions by ΣΠΣ formulas. By combining the proof of the FredmanKomlós bound [5, 10] and a counting argument, we show that for k and n large and k ≤ n/2, every ΣΠΣ formula computing the threshold function T n k has size at least exp(Ω(�k / ln k))n log n. For k and n large and k ≤ n2/3, we show that there exist ΣΠΣ formulas for computing T n k with size at most exp(2 √ k ln k)n log n. 1
The Random Adversary: A LowerBound Technique For Randomized Parallel Algorithms
 in Proc. of the 3rd SODA (ACM
, 1997
"... . The randomadversary technique is a general method for proving lower bounds on randomized parallel algorithms. The bounds apply to the number of communication steps, and they apply regardless of the processors' instruction sets, the lengths of messages, etc. This paper introduces the ra ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
.<F3.82e+05> The randomadversary technique is a general method for proving lower bounds on randomized parallel algorithms. The bounds apply to the number of communication steps, and they apply regardless of the processors' instruction sets, the lengths of messages, etc. This paper introduces the randomadversary technique and shows how it can be used to obtain lower bounds on randomized parallel algorithms for load balancing, compaction, padded sorting, and finding Hamiltonian cycles in random graphs. Using the randomadversary technique, we obtain the first lower bounds for randomized parallel algorithms which are provably faster than their deterministic counterparts (specifically, for load balancing and related problems).<F4.005e+05> Key words.<F3.82e+05> parallel algorithms, parallel computation, PRAM model, randomized parallel algorithms, expected time, lower bounds, load balancing<F4.005e+05> AMS subject classifications.<F3.82e+05> 68Q10, 68Q22, 68Q25<F4.005e+05> PII.<F3.82e+05> ...
Transforming comparison model lower bounds to the parallelrandomaccessmachine
 INFORMATION PROCESSING LETTERS
, 1997
"... We provide general transformations of lower bounds in Valiant's parallelcomparisondecisiontree model to lower bounds in the priority concurrentread concurrentwrite parallelrandomaccessmachine model. The proofs rely on standard Ramseytheoretic arguments that simplify the structure of the com ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
We provide general transformations of lower bounds in Valiant's parallelcomparisondecisiontree model to lower bounds in the priority concurrentread concurrentwrite parallelrandomaccessmachine model. The proofs rely on standard Ramseytheoretic arguments that simplify the structure of the computation by restricting the input domain. The transformation of comparison model lower bounds, which are usually easier to obtain, to the parallelrandomaccessmachine, unifies some known lower bounds and gives new lower bounds for several problems.
ERCW PRAMs and Optical Communication
 in Proceedings of the European Conference on Parallel Processing, EUROPAR ’96
, 1996
"... This paper presents algorithms and lower bounds for several fundamental problems on the Exclusive Read, Concurrent Write Parallel Random Access Machine (ERCW PRAM) and some results for unbounded fanin, bounded fanout (or `BFO') circuits. Our results for these two models are of importance because o ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
This paper presents algorithms and lower bounds for several fundamental problems on the Exclusive Read, Concurrent Write Parallel Random Access Machine (ERCW PRAM) and some results for unbounded fanin, bounded fanout (or `BFO') circuits. Our results for these two models are of importance because of the close relationship of the ERCW model to the OCPC model, a model of parallel computing based on dynamically reconfigurable optical networks, and of BFO circuits to the OCPC model with limited dynamic reconfiguration ability. Topics: Parallel Algorithms, Theory of Parallel and Distributed Computing. This research was supported by Texas Advanced Research Projects Grant 003658480. (philmac@cs.utexas.edu) y This research was supported in part by Texas Advanced Research Projects Grants 003658480 and 003658386, and NSF Grant CCR 9023059. (vlr@cs.utexas.edu) 1 Introduction In this paper we develop algorithms and lower bounds for fundamental problems on the Exclusive Read Concurrent Wri...
Simple Fast Parallel Hashing by Oblivious Execution
 AT&T Bell Laboratories
, 1994
"... A hash table is a representation of a set in a linear size data structure that supports constanttime membership queries. We show how to construct a hash table for any given set of n keys in O(lg lg n) parallel time with high probability, using n processors on a weak version of a crcw pram. Our algo ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
A hash table is a representation of a set in a linear size data structure that supports constanttime membership queries. We show how to construct a hash table for any given set of n keys in O(lg lg n) parallel time with high probability, using n processors on a weak version of a crcw pram. Our algorithm uses a novel approach of hashing by "oblivious execution" based on probabilistic analysis to circumvent the parity lower bound barrier at the nearlogarithmic time level. The algorithm is simple and is sketched by the following: 1. Partition the input set into buckets by a random polynomial of constant degree. 2. For t := 1 to O(lg lg n) do (a) Allocate M t memory blocks, each of size K t . (b) Let each bucket select a block at random, and try to injectively map its keys into the block using a random linear function. Buckets that fail carry on to the next iteration. The crux of the algorithm is a careful a priori selection of the parameters M t and K t . The algorithm uses only O(lg lg...
Some Topics in Parallel Computation and Branching Programs
, 1995
"... Some Topics in Parallel Computation and Branching Programs by Rakesh Kumar Sinha Chairperson of the Supervisory Committee: Professor Paul Beame Department of Computer Science and Engineering There are two parts of this thesis: the first part gives two constructions of branching programs; the second ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Some Topics in Parallel Computation and Branching Programs by Rakesh Kumar Sinha Chairperson of the Supervisory Committee: Professor Paul Beame Department of Computer Science and Engineering There are two parts of this thesis: the first part gives two constructions of branching programs; the second part contains three results on models of parallel machines. The branching program model has turned out to be very useful for understanding the computational behavior of problems. In addition, several restrictions of branching programs, for example ordered binary decision diagrams, have proven to be successful data structures in several VLSI design and verification applications. We construct a branching program of o(n log 3 n) nodes for computing any threshold function on n variables and a branching program of o(n log 4 n) nodes for determining the sum of n variables modulo a fixed divisor. These are improvements over constructions of size 2(n 3=2 ) due to Lupanov [Lup65]. The second p...