Long tours and short superstrings

Kosaraju, S. Rao; Park, J.K.; Stein, Clifford

doi:10.1109/sfcs.1994.365696

Cited by 63 publications

(57 citation statements)

References 10 publications

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“…Czumaj et al [6] re ned the algorithm of [22] to achieve a 2 5 6 approximation. Kosaraju et al obtained an improved result for the maximum traveling salesman problem; this more general result can be used by the algorithm of [4] to obtain an approximation slightly better than 2:8 [15]. Our result of 2 3 4 [2,1] was the best known until recently, and in fact can be combined with the algorithm of [15] to obtain an approximation ratio of about 2:725.…”

Section: Introductionmentioning

confidence: 55%

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A 2 2/3-approximation algorithm for the shortest superstring problem

Armen

Stein

1996

Combinatorial Pattern Matching

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Given a collection of strings S = fs 1 ; : : :; s n g over an alphabet , a superstring of S is a string containing each s i as a substring; that is, for each i, 1 i n, contains a block of js i j consecutive characters that match s i exactly. The shortest superstring problem is the problem of nding a superstring of minimum length. The shortest superstring problem has applications in both data compression and computational biology. In data compression, the problem is a part of a general model of string compression proposed by Gallant, Maier and Storer (JCSS '80). Much of the recent interest in the problem is due to its application to DNA sequence assembly.The problem has been shown to be NP-hard; in fact, it was shown by Blum et al.(JACM '94) to be MAX SNP-hard. The rst O(1)-approximation was also due to Blum et al., who gave an algorithm that always returns a superstring no more than 3 times the length of an optimal solution. Several researchers have published results that improve on the approximation ratio; of these, the best previous result is our algorithm ShortString, which achieves a 2 3 4 {approximation (WADS '95).We present our new algorithm, G-ShortString, which achieves a ratio of 2 2 3 . It generalizes the ShortString algorithm, but the analysis di ers substantially from that of ShortString. Our previous work identi ed classes of strings that have a nested periodic structure, and which must be present in the worst case for our algorithms. We introduced machinery to descibe these strings and proved strong structural properties about them. In this paper we extend this study to strings that exhibit a more relaxed form of the same structure, and we use this understanding to obtain our improved result.

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Section: Introductionmentioning

confidence: 55%

“…However, this correspondence breaks down for approximations; approximating the largest overlap appears to be an easier problem (cf. [23,22,15]) than approximating the shortest superstring.…”

Section: Preliminariesmentioning

confidence: 99%

A 2 2/3-approximation algorithm for the shortest superstring problem

Armen

Stein

1996

Combinatorial Pattern Matching

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“…Like the Minimum TSP, the Maximum TSP is also NP-hard, but differently from what happens for the Minimum TSP, it is approximable within a constant factor even when the distance matrix can be completely arbitrary. In the static setting, the best known result for Max TSP is a 0.6-approximation algorithm due to Kosaraju et al [25]. Once again, the knowledge of an optimum solution to the initial instance is useful, as the reoptimization problem under insertion of a vertex can be approximated within a ratio of 0.66 (for large enough n), as we show next.…”

Section: The Maximum Traveling Salesman Problemmentioning

confidence: 84%

“…While the typical applications of the Minimum TSP are in vehicle routing and transportation problems, the Maximum TSP has applications to DNA sequencing and data compression [25]. Like the Minimum TSP, the Maximum TSP is also NP-hard, but differently from what happens for the Minimum TSP, it is approximable within a constant factor even when the distance matrix can be completely arbitrary.…”

Section: The Maximum Traveling Salesman Problemmentioning

confidence: 99%

Complexity and Approximation

Ausiello¹,

Marchetti-Spaccamela²,

Crescenzi³

et al. 1999

717

336

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Abstract. In this survey the following model is considered. We assume that an instance I of a computationally hard optimization problem has been solved and that we know the optimum solution of such instance. Then a new instance I ′ is proposed, obtained by means of a slight perturbation of instance I. How can we exploit the knowledge we have on the solution of instance I to compute a (approximate) solution of instance I ′ in an efficient way? This computation model is called reoptimization and is of practical interest in various circumstances. In this article we first discuss what kind of performance we can expect for specific classes of problems and then we present some classical optimization problems (i.e. Max Knapsack, Min Steiner Tree, Scheduling) in which this approach has been fruitfully applied. Subsequently, we address vehicle routing problems and we show how the reoptimization approach can be used to obtain good approximate solution in an efficient way for some of these problems.

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“…SSP is known to be NP-hard [36]. A number of approximation algorithms with a fixed approximation ratio have been developed that use different variations of the greedy [1,15,17,33]. SSP is closely related to DNA-sequencing, which aims to sequence a strand of DNA from a set of "reads" (short fragments of the future superstring) whose locations in the strand are not known [49].…”

Section: Shortest Superstring Problemmentioning

confidence: 99%

Discovering optimization algorithms through automated learning

Breimer¹,

Goldberg²,

Hollinger³

et al. 2007

DIMACS Series in Discrete Mathematics And Theoretical Computer Science

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Abstract. In this paper, we describe the supervised learning approach to optimization problems in the spirit of the PAC learning model. By this approach, we discover domain-specific algorithms by learning from an oracle, which is also an optimization algorithm for the problem in question. We describe examples of learning backtracking-based algorithms and algorithms that implement the dynamic programming paradigm.

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Long tours and short superstrings

Cited by 63 publications

References 10 publications

A 2 2/3-approximation algorithm for the shortest superstring problem

A 2 2/3-approximation algorithm for the shortest superstring problem

Complexity and Approximation

Discovering optimization algorithms through automated learning

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