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92
Greed is Good: Approximating Independent Sets in Sparse and . . .
, 1994
"... ... for short, is one of the ~implest, most efficient, and most thoroughly studied methods for finding independent sets in graphs. We show that it surprisingly achieves a performance ratio of (A+ 2)/3 for approximating independent sets in graphs with degree bounded by A. The analysis directs us tow ..."
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Cited by 56 (7 self)
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... for short, is one of the ~implest, most efficient, and most thoroughly studied methods for finding independent sets in graphs. We show that it surprisingly achieves a performance ratio of (A+ 2)/3 for approximating independent sets in graphs with degree bounded by A. The analysis directs us towards a simple parallel and distributed algorithm with identical performance, which on constantdegree graphs runs in O(log ” n) time using linear number of processors. We also analyze the Greedy algorithm when run in combination with a fractional relaxation technique of Nemhauser and Trotter, and obtain an improved (2Z + 3)/5 performance ratio on graphs with average degree ~. Finally, we introduce a generally applicable technique for improving the approximation ratios of independent set algorithms, and illustrate it by improving the performance ratio of Greedy for large ∆.
An Improved Lower Bound for the Time Complexity of Mutual Exclusion (Extended Abstract)
 IN PROCEEDINGS OF THE 20TH ANNUAL ACM SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 2001
"... We establish a lower bound of 23 N= log log N) remote memory references for Nprocess mutual exclusion algorithms based on reads, writes, or comparison primitives such as testandset and compareand swap. Our bound improves an earlier lower bound of 32 log N= log log log N) established by Cyph ..."
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Cited by 41 (12 self)
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We establish a lower bound of 23 N= log log N) remote memory references for Nprocess mutual exclusion algorithms based on reads, writes, or comparison primitives such as testandset and compareand swap. Our bound improves an earlier lower bound of 32 log N= log log log N) established by Cypher. Our lower bound is of importance for two reasons. First, it almost matches the (log N) time complexity of the bestknown algorithms based on reads, writes, or comparison primitives. Second, our lower bound suggests that it is likely that, from an asymptotic standpoint, comparison primitives are no better than reads and writes when implementing localspin mutual exclusion algorithms. Thus, comparison primitives may not be the best choice to provide in hardware if one is interested in scalable synchronization.
Compactness results in extremal graph theory
 Combinatorica
, 1982
"... Dedicated to Tibor Gallai on his seventieth birthday ..."
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Cited by 34 (1 self)
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Dedicated to Tibor Gallai on his seventieth birthday
Minimum Color Sum of Bipartite Graphs
 Journal of Algorithms
, 1999
"... The problem of minimum color sum of a graph is to color the vertices of the graph such that the sum (average) of all assigned colors is minimum. Recently, in [BBH + 96], it was shown that in general graphs this problem cannot be approximated within n 1\Gammaffl , for any ffl ? 0, unless NP = ..."
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Cited by 29 (11 self)
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The problem of minimum color sum of a graph is to color the vertices of the graph such that the sum (average) of all assigned colors is minimum. Recently, in [BBH + 96], it was shown that in general graphs this problem cannot be approximated within n 1\Gammaffl , for any ffl ? 0, unless NP = ZPP . In the same paper, a 9=8approximation algorithm was presented for bipartite graphs. The hardness question for this problem on bipartite graphs was left open. In this paper we show that the minimum color sum problem for bipartite graphs admits no polynomial approximation scheme, unless P = NP . The proof is by Lreducing the problem of finding the maximum independent set in a graph whose maximum degree is four to this problem. This result indicates clearly that the minimum color sum problem is much harder than the traditional coloring problem which is trivially solvable in bipartite graphs. As for the approximation ratio, we make a further step towards finding the precise thr...
The chromatic number of Kneser hypergraphs
 Trans. Amer. Math. Soc
, 1986
"... Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at ..."
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Cited by 28 (3 self)
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Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at
Filtering algorithms for the NValue constraint
 In Proceedings CPAIOR’05
, 2005
"... Abstract. The constraint NValue counts the number of different values assigned to a vector of variables. Propagating generalized arc consistency on this constraint is NPhard. We show that computing even the lower bound on the number of values is NPhard. We therefore study different approximation h ..."
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Cited by 27 (10 self)
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Abstract. The constraint NValue counts the number of different values assigned to a vector of variables. Propagating generalized arc consistency on this constraint is NPhard. We show that computing even the lower bound on the number of values is NPhard. We therefore study different approximation heuristics for this problem. We introduce three new methods for computing a lower bound on the number of values. The first two are based on the maximum independent set problem and are incomparable to a previous approach based on intervals. The last method is a linear relaxation of the problem. This gives a tighter lower bound than all other methods, but at a greater asymptotic cost. 1 Introduction The NValue constraint counts the number of distinct values used by a vectorof variables. It is a generalization of the widely used AllDifferent constraint[12]. It was introduced in [4] to model a musical playlist configuration problem so
A time complexity bound for adaptive mutual exclusion
 In Proceedings of the 15th International Symposium on Distributed Computing
, 2001
"... ..."
Time/Contention Tradeoffs for Multiprocessor Synchronization
 Information and Computation
, 1996
"... We establish tradeoffs between time complexity and write and accesscontention for solutions to the mutual exclusion problem. The writecontention (accesscontention) of a concurrent program is the number of processes that may be simultaneously enabled to write (access by reading and/or writing) t ..."
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Cited by 23 (7 self)
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We establish tradeoffs between time complexity and write and accesscontention for solutions to the mutual exclusion problem. The writecontention (accesscontention) of a concurrent program is the number of processes that may be simultaneously enabled to write (access by reading and/or writing) the same shared variable. Our notion of time complexity distinguishes between local and remote accesses of shared memory. We show that, for any Nprocess mutual exclusion algorithm, if writecontention is w, and if at most v remote variables can be accessed by a single atomic operation, then there exists an execution involving only one process in which that process executes\Omega\Gammaecu vw N) remote operations for entry into its critical section. We further show that, among these operations,\Omega\Gamma p log vw N) distinct remote variables are accessed. For algorithms with accesscontention c, we show that the latter bound can be improved to \Omega\Gamma/51 vc N ). The last two of thes...
Improved Upper Bounds on Stopping Redundancy
, 2007
"... For a linear block code with minimum distance d, its stopping redundancy is the minimum number of check nodes in a Tanner graph representation of the code, such that all nonempty stopping sets have size d or larger. We derive new upper bounds on stopping redundancy for all linear codes in general, ..."
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Cited by 21 (3 self)
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For a linear block code with minimum distance d, its stopping redundancy is the minimum number of check nodes in a Tanner graph representation of the code, such that all nonempty stopping sets have size d or larger. We derive new upper bounds on stopping redundancy for all linear codes in general, and for maximum distance separable (MDS) codes specifically, and show how they improve upon previous results. For MDS codes, the new bounds are found by upperbounding the stopping redundancy by a combinatorial quantity closely related to Turán numbers. (The Turán number, „