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18
Workpreserving emulations of fixedconnection networks
 21st ACM Symp. on Theory of Computing
, 1989
"... Abstract. In this paper, we study the problem of emulating T G steps of an N Gnode guest network, G, on an N Hnode host network, H. We call an emulation workpreserving if the time required by the host, T H,isO(T GN G/N H), because then both the guest and host networks perform the same total work ..."
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Cited by 46 (18 self)
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Abstract. In this paper, we study the problem of emulating T G steps of an N Gnode guest network, G, on an N Hnode host network, H. We call an emulation workpreserving if the time required by the host, T H,isO(T GN G/N H), because then both the guest and host networks perform the same total work (i.e., processortime product), �(T GN G), to within a constant factor. We say that an emulation occurs in realtime if T H � O(T G), because then the host emulates the guest with constant slowdown. In addition to describing several workpreserving and realtime emulations, we also provide a general model in which lower bounds can be proved. Some of the more interesting and diverse consequences of this work include: (1) a proof that a linear array can emulate a (much larger) butterfly in a workpreserving fashion, but that a butterfly cannot emulate an expander (of any size) in a workpreserving fashion, (2) a proof that a butterfly can emulate a shuffleexchange network in a realtime workpreserving fashion, and vice versa, (3) a proof that a butterfly can emulate a mesh (or an array of higher, but fixed, dimension) in a realtime workpreserving fashion, even though any O(1)to1 embedding of an Nnode mesh in an Nnode butterfly has dilation �(log N), and
Generating Linear Extensions Fast
"... One of the most important sets associated with a poset P is its set of linear extensions, E(P) . "ExtensionFast.html" 87 lines, 2635 characters One of the most important sets associated with a poset P is its set of linear extensions, E(P) . In this paper, we present an algorithm to generate all of t ..."
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Cited by 36 (6 self)
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One of the most important sets associated with a poset P is its set of linear extensions, E(P) . "ExtensionFast.html" 87 lines, 2635 characters One of the most important sets associated with a poset P is its set of linear extensions, E(P) . In this paper, we present an algorithm to generate all of the linear extensions of a poset in constant amortized time; that is, in time O(e(P)) , where e ( P ) =  E(P) . The fastest previously known algorithm for generating the linear extensions of a poset runs in time O(n e(P)) , where n is the number of elements of the poset. Our algorithm is the first constant amortized time algorithm for generating a ``naturally defined'' class of combinatorial objects for which the corresponding counting problem is #Pcomplete. Furthermore, we show that linear extensions can be generated in constant amortized time where each extension differs from its predecessor by one or two adjacent transpositions. The algorithm is practical and can be modified to efficiently count linear extensions, and to compute P(x < y) , for all pairs x,y , in time O( n^2 + e ( P )).
Algorithms for Square Roots of Graphs
 SIAM Journal on Discrete Mathematics
, 1991
"... The nth power (n 1) of a graph G = (V; E), written G n , is defined to be the graph having V as its vertex set with two vertices u; v adjacent in G n if and only if there exists a path of length at most n between them. Similarly, graph H has an nth root G if G n = H . For the case of n = 2, ..."
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Cited by 34 (0 self)
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The nth power (n 1) of a graph G = (V; E), written G n , is defined to be the graph having V as its vertex set with two vertices u; v adjacent in G n if and only if there exists a path of length at most n between them. Similarly, graph H has an nth root G if G n = H . For the case of n = 2, we say that G 2 is the square of G and G is the square root of G 2 . Here we give a linear time algorithm for finding the tree square roots of a given graph and a linear time algorithm for finding the square roots of planar graphs. We also give a polynomial time algorithm for finding the square roots of subdivision graphs, which is equivalent to the problem of the inversion of total graphs. Further, we give a linear time algorithm for finding a Hamiltonian cycle in a cubic graph, and we prove the NPcompleteness of finding the maximum cliques in powers of graphs and the chordality of powers of trees. Keywords: Square graphs, power graphs, tree square, planar square graphs. 1 Introduct...
Computing Roots of Graphs is Hard
 DISCRETE APPLIED MATHEMATICS
, 1994
"... The square of an undirected graph G is the graph G² on the same vertex set such that there is an edge between two vertices in G² if and only if they are at distance at most 2 in G. The k'th power of a graph is defined analogously. It has been conjectured that the problem of computing any square r ..."
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Cited by 25 (1 self)
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The square of an undirected graph G is the graph G² on the same vertex set such that there is an edge between two vertices in G² if and only if they are at distance at most 2 in G. The k'th power of a graph is defined analogously. It has been conjectured that the problem of computing any square root of a square graph, or even that of deciding whether a graph is a square, is NPhard. We settle this conjecture in the affirmative.
WaferScale Integration of Systolic Arrays
 IEEE Transactions on Computers
, 1985
"... AbstractVLSI technologists are fast developing waferscale integration. Rather than partitioning a silicon wafer into chips as is usually done, the idea behind waferscale integration is to assemble an entire system (or network of chips) on a single wafer, thus avoiding the costs and performance lo ..."
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Cited by 17 (0 self)
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AbstractVLSI technologists are fast developing waferscale integration. Rather than partitioning a silicon wafer into chips as is usually done, the idea behind waferscale integration is to assemble an entire system (or network of chips) on a single wafer, thus avoiding the costs and performance loss associated with individual packaging of chips. A major problem with assembling a large system of microprocessors on a single wafer, however, is that some of the processors, or cells, on the wafer are likely to be defective. In the paper, we describe practical procedures for integrating "around " such faults. The procedures are designed to minimize the length of the longest wire in the system, thus minimizing the communication time between cells. Although the underlying network problems are NPcomplete, we prove that the procedures are reliable by assuming a probabilistic model of cell failure. We also discuss applications of the work to problems in VLSI layout theory, graph theory, faulttolerant systems, planar geometry, and the probabilistic analysis of algorithms. Index Terms Channel width, faulttolerant systems, matching, probabilistic analysis, spanning tree, systolic arrays, traveling salesman problem, tree of meshes, VLSI, waferscale integration, wire length. I.
Communication in wireless networks with directional antennae
 Proc. of the 20th Symp. on Parallelism in Algorithms and Architectures, Proc. of SPAA
, 2008
"... We study the problem of maintaining connectivity in a wireless network where the network nodes are equipped with directional antennas. Nodes correspond to points on the plane and each uses a directional antenna modeled by a sector with a given angle and radius. The connectivity problem is to decide ..."
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Cited by 10 (3 self)
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We study the problem of maintaining connectivity in a wireless network where the network nodes are equipped with directional antennas. Nodes correspond to points on the plane and each uses a directional antenna modeled by a sector with a given angle and radius. The connectivity problem is to decide whether or not it is possible to orient the antennas so that the directed graph induced by the node transmissions is strongly connected. We present algorithms for simple polynomialtimesolvable cases of the problem, show that the problem is NPcomplete in the 2dimensional case when the sector angle is small, and present algorithms that approximate the minimum radius to achieve connectivity for sectors with a given angle. We also discuss several extensions to related problems. To the best of our knowledge, the problem has not been studied before in the literature.
ClawFree Graphs  a Survey.
, 1996
"... In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden subgraph ..."
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Cited by 9 (1 self)
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In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden subgraphs e) Invariants f) Squares g) Regular graphs h) Other hamiltonicity related results and generalizations 3. Matchings and factors 4. Independence, domination, other invariants and extremal problems 5. Algorithmic aspects 6. Miscellaneous 7. Appendix  List of all 2connected nonhamiltonian clawfree graphs on n 12 vertices. 1 This research was done while the first and second author were visiting Univ. of West Bohemia and while the third author was visiting L.R.I. and Memphis State University. 2 Research partially supported by ONR Grant N00014 91J1085 and NSA MDA 90490H4034. 3 Research supported by EC grant No.192493. 1 1. INTRODUCTION Clawfree graphs have been a su...
Performance Guarantees for the TSP with a Parameterized Triangle Inequality
 IN PROC. 6TH INT. WORKSHOP ON ALGORITHMS AND DATA STRUCTURES (WADS), VOLUME 1663 OF LECTURE NOTES IN COMPUT. SCI
, 2000
"... We consider the approximability of the tsp problem in graphs that satisfy a relaxed form of triangle inequality. More precisely, we assume that for some parameter 1, the distances satisfy the inequality dist(x; y) \Delta (dist(x; z) + dist(z; y)) for every triple of vertices x, y, and z. We o ..."
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Cited by 8 (0 self)
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We consider the approximability of the tsp problem in graphs that satisfy a relaxed form of triangle inequality. More precisely, we assume that for some parameter 1, the distances satisfy the inequality dist(x; y) \Delta (dist(x; z) + dist(z; y)) for every triple of vertices x, y, and z. We obtain a 4 approximation and also show that for some ffl ? 0 it is nphard to obtain a (1 + ffl ) approximation. Our upper bound improves upon the earlier known ratio of (3 =2 + =2) [1] for all values of ? 7/3.
Approximation Algorithms for Structured Communication Problems
 In 9th ACM Symposium on Parallel Algorithms and Architectures (SPAA '97
, 1997
"... Given a network of processors, a structured communication problem consists to route a communication pattern known in advance. Structured communication problems appear frequently in parallel computing. Hence, communication libraries (e.g, PVM or MPI) generally include a specific access to procedures ..."
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Cited by 6 (4 self)
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Given a network of processors, a structured communication problem consists to route a communication pattern known in advance. Structured communication problems appear frequently in parallel computing. Hence, communication libraries (e.g, PVM or MPI) generally include a specific access to procedures solving the most common problems of this type. A standard communication model assumes that information proceeds by a sequence of calls between neighboring nodes of the network, and that each node is allowed to call at most one neighbor at a time. In this context, most of the decision problems corresponding to the usual structured communication problems have been shown to be NPcomplete. Therefore, several approximation algorithms have been proposed to solve specific problems. Each of these algorithms is dedicated to a particular problem. In this paper, we present a high level method which can be used to derive approximation algorithms for many different structured communication problems on ...
Cycles in Networks
, 1993
"... We study the presence of cycles and long paths in graphs that have been proposed as interconnection networks for parallel architectures. The study surveys and complements known results. 1 Introduction This paper is devoted to studying embeddings of the simplest possible guest graphs, the path P ..."
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Cited by 6 (0 self)
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We study the presence of cycles and long paths in graphs that have been proposed as interconnection networks for parallel architectures. The study surveys and complements known results. 1 Introduction This paper is devoted to studying embeddings of the simplest possible guest graphs, the path PN and the cycle CN , in graphs that have been proposed as interconnection networks for parallel architectures. In addition to their intrinsic interest, in terms of the development of algorithms on parallel architectures, these two guest graphs are important because of the fact that many structurally richer graphs can be constructed from paths and cycles by various product constructions. A few of the results we present are original; several appear in the literature and are duly cited; many belong to the folklore of the field. Indeed this paper is motivated by a desire to find a single repository for this important, yet scattered material. Before proceeding further, we define formally the ...