The Directed Steiner Network problem is tractable for a constant number of terminals

Feldman, Jon; Ruhl, Matthias

doi:10.1109/sffcs.1999.814601

Cited by 16 publications

(23 citation statements)

References 8 publications

(7 reference statements)

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“…However, two questions naturally arise. First, if the size of the query is bounded, the Steiner-tree problem is tractable [8,5]. So, can the top-k answers be computed efficiently under data complexity?…”

Section: Introductionmentioning

confidence: 99%

Finding and approximating top-k answers in keyword proximity search

Kimelfeld

Sagiv

2006

Proceedings of the Twenty-Fifth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

130

147

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Various approaches for keyword proximity search have been implemented in relational databases, XML and the Web. Yet, in all of them, an answer is a Q-fragment, namely, a subtree T of the given data graph G, such that T contains all the keywords of the query Q and has no proper subtree with this property. The rank of an answer is inversely proportional to its weight. Three problems are of interest: finding an optimal (i.e., top-ranked) answer, computing the top-k answers and enumerating all the answers in ranked order. It is shown that, under data complexity, an efficient algorithm for solving the first problem is sufficient for solving the other two problems with polynomial delay. Similarly, an efficient algorithm for finding a θ-approximation of the optimal answer suffices for carrying out the following two tasks with polynomial delay, under query-and-data complexity. First, enumerating in a (θ + 1)-approximate order. Second, computing a (θ + 1)-approximation of the top-k answers. As a corollary, this paper gives the first efficient algorithms, under data complexity, for enumerating all the answers in ranked order and for computing the top-k answers. It also gives the first efficient algorithms, under query-and-data complexity, for enumerating in a provably approximate order and for computing an approximation of the top-k answers.

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Section: Introductionmentioning

confidence: 99%

Finding and approximating top-k answers in keyword proximity search

Kimelfeld

Sagiv

2006

Proceedings of the Twenty-Fifth ACM SIGMOD-SIGACT-SIGART Symposium on Principles of Database Systems

130

147

View full text Add to dashboard Cite

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“…McCormick [17] proved that the problem r s 1 t 1 = r s 2 t 2 = k (r i j = 0 otherwise) on a directed graph is NP-hard, when k is part of the input. When k = 1 Li, McCormick, and Simchi-Levi [16] showed that the problem is polynomially solvable, and Natu and Fang [20,21], and Feldman and Ruhl [6] describe more efficient solutions. The latter authors also proved that the problem is polynomially solvable for any constant k. A simple modification of the reduction in [16] can be used to show that the problem is hard even when r s 1 t 1 = k and r s 2 t 2 = 1.…”

Section: Directed K-path Tree Problemsmentioning

confidence: 99%

The k-path tree matroid and its applications to survivable network design

Arkin

Hassin

2008

Discrete Optimization

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We define the k-path tree matroid, and use it to solve network design problems in which the required connectivity is arbitrary for a given pair of nodes, and 1 for the other pairs. We solve the problems for undirected and directed graphs. We then use these exact algorithms to give improved approximation algorithms for problems in which the weights satisfy the triangle inequality and the connectivity requirement is either 2 among at most five nodes and 1 for the other nodes, or it is 3 among a set of three nodes and 1 for all other nodes.

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“…Note that this problem is an instance of the point-to-point connection problem (Feldman and Ruhl, 1999), where the source-destination pairs are those pairs .s; t/ with t up and to the right of s. Since we can restrict the grid to the Hanan grid of the input terminals and since there are O.n 2 / upright pairs for an input terminal set N of size n, the algorithm of Feldman and Ruhl (1999) gives an O.n 2n / algorithm for nding the optimal minimum network. We now modify the algorithm from Gudmundsson et al (2001) to give an O.n 3 / 2-approximation algorithm.…”

Section: A 2-approximation Algorithm For Manhattan Network On Alignmmentioning

confidence: 99%

Picking Alignments from (Steiner) Trees

Lam

Alexandersson

Pachter

2003

Journal of Computational Biology

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The application of Needleman-Wunsch alignment techniques to biological sequences is complicated by two serious problems when the sequences are long: the running time, which scales as the product of the lengths of sequences, and the difficulty in obtaining suitable parameters that produce meaningful alignments. The running time problem is often corrected by reducing the search space, using techniques such as banding, or chaining of high-scoring pairs. The parameter problem is more difficult to fix, partly because the probabilistic model, which Needleman-Wunsch is equivalent to, does not capture a key feature of biological sequence alignments, namely the alternation of conserved blocks and seemingly unrelated nonconserved segments. We present a solution to the problem of designing efficient search spaces for pair hidden Markov models that align biological sequences by taking advantage of their associated features. Our approach leads to an optimization problem, for which we obtain a 2-approximation algorithm, and that is based on the construction of Manhattan networks, which are close relatives of Steiner trees. We describe the underlying theory and show how our methods can be applied to alignment of DNA sequences in practice, successfully reducing the Viterbi algorithm search space of alignment PHMMs by three orders of magnitude.

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The Directed Steiner Network problem is tractable for a constant number of terminals

Abstract: We consider the DIRECTED STEINER NETWORK problem, also called the POINT-TO-POINT CONNECTION problem, where given a directed graph G and p pairs

Cited by 16 publications

References 8 publications

Finding and approximating top-k answers in keyword proximity search

Finding and approximating top-k answers in keyword proximity search

The k-path tree matroid and its applications to survivable network design

Picking Alignments from (Steiner) Trees

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