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117
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 ∆.
Analysis of Gene Expression Microarrays for Phenotype Classification
 Proc. Int. Conf. Intell. Syst. Mol. Biol
, 2000
"... Several microarray technologies that monitor the level of expression of a large number of genes have recently emerged. Given DNAmicroarray data for a set of cells characterized by a given phenotype and for a set of control cells, an important problem is to identify "patterns" of gene expressio ..."
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Cited by 53 (6 self)
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Several microarray technologies that monitor the level of expression of a large number of genes have recently emerged. Given DNAmicroarray data for a set of cells characterized by a given phenotype and for a set of control cells, an important problem is to identify "patterns" of gene expression that can be used to predict cell phenotype. The potential number of such patterns is exponential in the number of genes. In this paper, we propose a solution to this problem based on a supervised learning algorithm, which differs substantially from previous schemes. It couples a complex, nonlinear similarity metric, which maximizes the probability of discovering discriminative gene expression patterns, and a pattern discovery algorithm called SPLASH. The latter discovers efficiently and deterministically all statistically significant gene expression patterns in the phenotype set. Statistical significance is evaluated based on the probability of a pattern to occur by chance in ...
Improved Approximation Guarantees for Packing and Covering Integer Programs
 SIAM J. Comput
, 1995
"... Several important NPhard combinatorial optimization problems can be posed as packing/covering integer programs; the randomized rounding technique of Raghavan & Thompson is a powerful tool to approximate them well. We present one elementary unifying property of all these integer programs (IPs), and ..."
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Cited by 43 (6 self)
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Several important NPhard combinatorial optimization problems can be posed as packing/covering integer programs; the randomized rounding technique of Raghavan & Thompson is a powerful tool to approximate them well. We present one elementary unifying property of all these integer programs (IPs), and use the FKG correlation inequality to derive an improved analysis of randomized rounding on them. This also yields a pessimistic estimator, thus presenting deterministic polynomialtime algorithms for them with approximation guarantees significantly better than those known. Keywords.Approximation Algorithms, Combinatorial Optimization, Correlation Inequalities, Covering Integer Programs, Derandomization, Integer Programming, Linear Programming, Linear Relaxations, Packing Integer Programs, Positive Correlation, Randomized Rounding, Rounding Theorems. 1 Preliminary versions of this work appeared in the Proc. ACM Symposium on the Theory of Computing, pages 268276, 1995, and as DIMACS Te...
Network Lifetime and Power Assignment in AdHoc Wireless Networks
 in ESA
, 2003
"... Abstract. Used for topology control in adhoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanni ..."
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Cited by 42 (3 self)
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Abstract. Used for topology control in adhoc wireless networks, Power Assignment is a family of problems, each defined by a certain connectivity constraint (such as strong connectivity) The input consists of a directed complete weighted graph G = (V; c). The power of a vertex u in a directed spanning subgraph H is given by pH(u) = maxuv2E(H) c(uv). The power of H is given by p(H) = P u2V pH(u), Power Assignment seeks to minimize p(H) while H satisfies the given connectivity constraint. We
Feedback set problems
 HANDBOOK OF COMBINATORIAL OPTIMIZATION
, 1999
"... ABSTRACT. This paper is a short survey of feedback set problems. It will be published in ..."
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Cited by 36 (1 self)
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ABSTRACT. This paper is a short survey of feedback set problems. It will be published in
Computing NearOptimal Solutions to Combinatorial Optimization Problems
 IN COMBINATORIAL OPTIMIZATION, DIMACS SERIES IN DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
, 1995
"... In the past few years, there has been significant progress in our understanding of the extent to which nearoptimal solutions can be efficiently computed for NPhard combinatorial optimization problems. This paper surveys these recent developments, while concentrating on the advances made in the ..."
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Cited by 31 (0 self)
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In the past few years, there has been significant progress in our understanding of the extent to which nearoptimal solutions can be efficiently computed for NPhard combinatorial optimization problems. This paper surveys these recent developments, while concentrating on the advances made in the design and analysis of approximation algorithms, and in particular, on those results that rely on linear programming and its generalizations.
An Extension of the Lovász Local Lemma, and its Applications to Integer Programming
 In Proceedings of the 7th Annual ACMSIAM Symposium on Discrete Algorithms
, 1996
"... The Lov'asz Local Lemma (LLL) is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events, each of which asserts that a random variable does not deviate much from its mea ..."
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Cited by 31 (6 self)
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The Lov'asz Local Lemma (LLL) is a powerful tool in proving the existence of rare events. We present an extension of this lemma, which works well when the event to be shown to exist is a conjunction of individual events, each of which asserts that a random variable does not deviate much from its mean. We consider three classes of NPhard integer programs: minimax, packing, and covering integer programs. A key technique, randomized rounding of linear relaxations, was developed by Raghavan & Thompson to derive good approximation algorithms for such problems. We use our extended LLL to prove that randomized rounding produces, with nonzero probability, much better feasible solutions than known before, if the constraint matrices of these integer programs are sparse (e.g., VLSI routing using short paths, problems on hypergraphs with small dimension/degree). We also generalize the method of pessimistic estimators due to Raghavan, to constructivize our packing and covering results. 1
Polynomialtime Learning of Elementary Formal Systems
 Theoretical Computer Science
, 2000
"... An elementary formal system (EFS) is a logic program con sisting of definite clauses whose arguments have patterns instead of firstorder terms. We investigate EFSs for polynomialtime PAClearnability. A definite clause of an EFS is hereditary if every pattern in the body is a subword of a pat ..."
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Cited by 30 (7 self)
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An elementary formal system (EFS) is a logic program con sisting of definite clauses whose arguments have patterns instead of firstorder terms. We investigate EFSs for polynomialtime PAClearnability. A definite clause of an EFS is hereditary if every pattern in the body is a subword of a pattern in the head. With this new notion, we show that HEFS(ra, k, t, r) is polynomialtime learnable, which is the class of languages definable by EFSs consisting of at most ra hereditary definite clauses with predicate symbols of arity at most r, where k and t bound the number of variable occurrences in the head and the number of atoms in the body, respectively. The class defined by all finite unions of EFSs in HEFS(ra, k, t, r) is also polynomialtime learnable. We also show an interesting series of NClearnable classes of EFSs. As hardness results, the class of regular pattern languages is shown not polynomialtime learnable unless RP=NP. Furthermore, the related problem of deciding whether there is a common subsequence which is consistent with given positive and negative examples is shown NPcomplete.
Complexity and Approximation of Fixing Numerical Attributes in Databases Under Integrity Constraints
 In International Workshop on Database Programming Languages
, 2005
"... Abstract. Consistent query answering is the problem of computing the answers from a database that are consistent with respect to certain integrity constraints that the database as a whole may fail to satisfy. Those answers are characterized as those that are invariant under minimal forms of restorin ..."
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Cited by 30 (12 self)
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Abstract. Consistent query answering is the problem of computing the answers from a database that are consistent with respect to certain integrity constraints that the database as a whole may fail to satisfy. Those answers are characterized as those that are invariant under minimal forms of restoring the consistency of the database. In this context, we study the problem of repairing databases by fixing integer numerical values at the attribute level with respect to denial and aggregate constraints. We introduce a quantitative definition of database fix, and investigate the complexity of several problems such as DFP, i.e. the existence of fixes within a given distance from the original instance, and CQA, i.e. deciding consistency of answers to aggregate conjunctive queries under different semantics. We provide sharp complexity bounds, identify relevant tractable cases; and introduce approximation algorithms for some of those that are intractable. More specifically, we obtain results like undecidability of existence of fixes for aggregate constraints; MAXSNPhardness of DFP, but a good approximation algorithm for a relevant special case; and intractability but good approximation for CQA for aggregate queries for one database atom denials (plus builtins). 1
A Formal Framework For The Study Of Task Allocation In MultiRobot Systems
, 2003
"... Despite more than a decade of experimental work in multirobot systems, important theoretical aspects of multirobot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multirobot task allocation (MRTA). Most work on MRTA has been ad hoc ..."
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Cited by 28 (6 self)
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Despite more than a decade of experimental work in multirobot systems, important theoretical aspects of multirobot coordination mechanisms have, to date, been largely untreated. To address this issue, we focus on the problem of multirobot task allocation (MRTA). Most work on MRTA has been ad hoc and empirical, with many coordination architectures having been proposed and validated in a proofofconcept fashion, but infrequently analyzed. With the goal of bringing objective grounding to this important area of research, we present a formal study of MRTA problems. A domainindependent taxonomy of MRTA problems is given, and it is shown how many such problems can be viewed as instances of other, wellstudied, optimization problems. We demonstrate how relevant theory from operations research and combinatorial optimization can be used for analysis and greater understanding of existing approaches to task allocation, and show how the same theory can be used in the synthesis of new approaches.