On the Approximation of Finding A(nother) Hamiltonian Cycle in Cubic Hamiltonian Graphs

Bazgan, Cristina; Sántha, Miklós; Tuza, Źsolt

doi:10.1006/jagm.1998.0998

Cited by 25 publications

(14 citation statements)

References 15 publications

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“…Showing that Pigeonhole Subset-Sums (a total function) is better approximable than the corresponding NP search problem is somewhat analogous to the result we have obtained in [1]. There we have shown that there is a polynomial-time approximation scheme for finding another Hamiltonian cycle in cubic Hamiltonian graphs if a Hamiltonian cycle is given in the input (again a total function).…”

Section: Introductionsupporting

confidence: 50%

“…From these differences smaller than 3K/n, we choose every second one (in the order of their occurrence) and create the sequence a (1) 1 < a (1) 2 < ··· < a (1) n (1) , to which we adjoin a (1) 0 =0. We also set K (1) =a (1) n (1) , where K (1) < 3K/n and n (1) \ n/3. We repeat this type of difference selection t=Nlog 3 nM times, creating the sequences /3.…”

Section: W(log N)mentioning

confidence: 99%

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Efficient Approximation Algorithms for the Subset-Sums Equality Problem

Bazgan¹,

Sántha²,

Tuza³

2002

Journal of Computer and System Sciences

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We investigate the problem of finding two nonempty disjoint subsets of a set of n positive integers, with the objective that the sums of the numbers in the two subsets be as close as possible. In two versions of this problem, the quality of a solution is measured by the ratio and the difference of the two partial sums, respectively. Answering a problem of G. J. Woeginger and Z. Yu (1992, Inform. Process. Lett. 42, 299-302) in the affirmative, we give a fully polynomial-time approximation scheme for the case where the value to be optimized is the ratio between the sums of the numbers in the two sets. On the other hand, we show that in the case where the value of a solution is the positive difference between the two partial sums, the problem is not 2 n k -approximable in polynomial time unless P=NP, for any constant k. In the positive direction, we give a polynomial time algorithm that finds two subsets for which the difference of the two sums does not exceed K/n W(log n) , where K is the greatest number in the instance.

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Section: Introductionsupporting

confidence: 50%

Section: W(log N)mentioning

confidence: 99%

Efficient Approximation Algorithms for the Subset-Sums Equality Problem

Bazgan¹,

Sántha²,

Tuza³

2002

Journal of Computer and System Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Showing that Pigeonhole Subset-Sums (a total function) is better approximable than the corresponding N P search problem is somewhat analogous to the result we have obtained in [1]. There we have shown that there is a polynomial-time approximation scheme for finding another Hamiltonian cycle in cubic Hamiltonian graphs if a Hamiltonian cycle is given in the input (again a total function).…”

Section: Introductionsupporting

confidence: 72%

Efficient approximation algorithms for the subset-sums equality problem

Bazgan

Sántha

Tuza

1998

Lecture Notes in Computer Science

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Abstract. We investigate the problem of finding two nonempty disjoint subsets of a set of n positive integers, with the objective that the sums of the numbers in the two subsets be as close as possible. In two versions of this problem, the quality of a solution is measured by the ratio and the difference of the two partial sums, respectively. Answering a problem of Woeginger and Yu (1992) in the affirmative, we give a fully polynomial-time approximation scheme for the case where the value to be optimized is the ratio between the sums of the numbers in the two sets. On the other hand, we show that in the case where the value of a solution is the positive difference between the two partial sums, the problem is not 2 n k -approximable in polynomial time unless P =N P , for any constant k. In the positive direction, we give a polynomial-time algorithm that finds two subsets for which the difference of the two sums does not exceed K/n Ω(log n) , where K is the greatest number in the instance.

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“…Thus the problem of maximizing adversarial infection is as hard to approximate as the longest path on regular graphs. Even in 3-regular Hamiltonian graphs, the longest-path problem is known not to have any constant factor approximation, unless P = NP [5].…”

Section: Theorem 1 the Adversarial Maximization Problem Ismentioning

confidence: 99%

On the Power of Adversarial Infections in Networks

Brautbar

Draief

Khanna

2013

Lecture Notes in Computer Science

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Abstract. Over the last decade we have witnessed the rapid proliferation of online networks and Internet activity. Such activity is considered as a blessing but it brings with it a large increase in risk of computer malware -malignant software that actively spreads from one computer to another. To date, the majority of existing models of malware spread use stochastic behavior, when the set of neighbors infected from the current set of infected nodes is chosen obliviously. In this work, we initiate the study of adversarial infection strategies which can decide intelligently which neighbors of infected nodes to infect next in order to maximize their spread, while maintaining a similar "signature" as the oblivious stochastic infection strategy as not to be discovered. We first establish that computing an optimal and near-optimal adversarial strategies is computational hard. We then identify necessary and sufficient conditions in terms of network structure and edge infection probabilities such that the adversarial process can infect polynomially more nodes than the stochastic process while maintaining a similar "signature" as the oblivious stochastic infection strategy. Among our results is a surprising connection between an additional structural quantity of interest in a network, the network toughness, and adversarial infections. Based on the network toughness, we characterize networks where existence of adversarial strategies that are pandemic (infect all nodes) is guaranteed, as well as efficiently computable.

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On the Approximation of Finding A(nother) Hamiltonian Cycle in Cubic Hamiltonian Graphs

Cited by 25 publications

References 15 publications

Efficient Approximation Algorithms for the Subset-Sums Equality Problem

Efficient Approximation Algorithms for the Subset-Sums Equality Problem

Efficient approximation algorithms for the subset-sums equality problem

On the Power of Adversarial Infections in Networks

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