A Search Procedure for Hamilton Paths and Circuits

Rubin, Frank

doi:10.1145/321850.321854

Cited by 55 publications

(31 citation statements)

References 4 publications

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“…If an instance has no tour, we call it infeasible. Observation 1 gives two sufficient conditions for an instance to be infeasible, as observed by Rubin [14].…”

Section: Reduction Rulesmentioning

confidence: 87%

“…We employ a known generalization of the TSP proposed by Rubin [14], named the forced Traveling Salesman Problem by Eppstein [5]. We define an instance I = (G, F) that consists of a simple, edge weighted, undirected graph G, and a subset F of edges in G, called forced.…”

Section: Preliminariesmentioning

confidence: 99%

“…Eppstein [5] started the exploration into polynomial space TSP algorithms specialized for graphs of bounded degree by designing an algorithm for degree-3 graphs that runs in O * (1.260 n ) time. He introduced a branch-and-search method by considering a generalization of the TSP proposed by Rubin [14], called the forced TSP. Iwama and Nakashima [11] claimed an improvement of Eppstein's time bound to O * (1.251 n )…”

Section: Introductionmentioning

confidence: 99%

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An Improved-time Polynomial-space Exact Algorithm for TSP in Degree-5 Graphs

Yunos

Shurbevski

Nagamochi

2017

Journal of Information Processing

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Abstract:The Traveling Salesman Problem (TSP) is one of the most well-known NP-hard optimization problems. Following a recent trend of research which focuses on developing algorithms for special types of TSP instances, namely graphs of limited degree, in an attempt to reduce a part of the time and space complexity, we present a polynomialspace branching algorithm for the TSP in an n-vertex graph with degree at most 5, and show that it has a running time of O * (2.3500 n ), which improves the previous best known time bound of O * (2.4723 n ) given by the authors (the 12 th International Symposium on Operations Research and Its Application (ISORA 2015(ISORA ), pp.45-58, 2015. While the base of the exponent in the running time bound of our algorithm is greater than 2, it still outperforms Gurevich and Shelah's O * (4 n n log n ) polynomial-space exact algorithm for the TSP in general graphs (SIAM Journal of Computation, Vol.16, No.3, pp.486-502, 1987). In the analysis of the running time, we use the measure-and-conquer method, and we develop a set of branching rules which foster the analysis of the running time.

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“…If an instance has no tour, we call it infeasible. Observation 1 gives two sufficient conditions for an instance to be infeasible, as observed by Rubin [14].…”

Section: Reduction Rulesmentioning

confidence: 87%

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An Improved-time Polynomial-space Exact Algorithm for TSP in Degree-5 Graphs

Yunos

Shurbevski

Nagamochi

2017

Journal of Information Processing

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“…For finding Hamiltonian cycles in general graphs, Rubin first presented a multi-path method which is an exhaustive search method [6]. Then, William Kocay introduced an algorithm that overlays additional pruning capabilities into the search [7].…”

Section: Introduction Backgroundmentioning

confidence: 99%

An Algorithm for Computing a Hamiltonian Cycle of Given Points in a Polygonal Region

Jia¹,

Jiang²

2018

dtcse

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In this paper, for a point set X in a simple polygon P, we present an algorithm to compute a Hamiltonian cycle which avoids the boundary of P and accesses all points of X. Computing a Hamiltonian cycle of given points in a simple polygon is a novel transformation of the general Hamiltonian problems and the problem of finding simple paths on given obstacles in a simple polygon. In our solution, we first construct the geodesic convex hull G of X inside P, and then find simple paths turn only at the points of X for two adjacent vertices in X along the boundary of G which are invisible to each other. After an original Hamiltonian cycle is found, we insert the remaining points to it. Finally, we present an O((n 2 +m)nlogm) time algorithm (n is the number of points in X and m is the number of P's vertices) to report a Hamiltonian cycle if it exists or report that no such cycle exists.

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“…The possibility that DNA computation could be applied to solving complex mathematical problems was demonstrated by a landmark work published in Science in 1994 [4]. In that paper, Adlemen proved that a biological system could be used to solve a seven-node instance of Directed Hamiltonian path (DHP) problem [5], which is known to be one of the difficult mathematical problems. This computational breakthrough stimulated imaginative studies by computer scientists and molecular biologists worldwide on topics such as combinatorial optimization, operations research and numerical computation with biological paradigms.…”

Section: Introductionmentioning

confidence: 99%

Biomolecular computing: Is it ready to take off?

2007

Biotechnology Journal

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Biomolecular computing is an emerging field at the interface of computer science, biological science and engineering. It uses DNA and other biological materials as the building blocks for construction of living computational machines to solve difficult combinatorial problems. In this article, notable advances in the biomolecular computing are reviewed and challenges associated with this multidisciplinary research are addressed. Finally, several perspectives are given based on the review of biomolecular computing.K Ke ey yw wo or rd ds s: Biocomputing · DNA strand · Massive parallelism · Self-assembling · Steganography C Co or rr re es sp po on nd de en nc ce e: Professor Pengcheng Fu, Department of Molecular Biosciences and Bioengineering, University of Hawaii at Manoa, 1955 East-West Road, Honolulu, HI 96822, USA E E--m ma ai il l: pengchen@hawaii.edu F Fa ax x: +1-808-956-3542 A Ab bb br re ev vi ia at ti io on ns s: D DH HP P, directed Hamiltonian path; N NP P, non-deterministic polynomial time; P PN NA A, peptide nucleic acid

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A Search Procedure for Hamilton Paths and Circuits

Cited by 55 publications

References 4 publications

An Improved-time Polynomial-space Exact Algorithm for TSP in Degree-5 Graphs

An Improved-time Polynomial-space Exact Algorithm for TSP in Degree-5 Graphs

An Algorithm for Computing a Hamiltonian Cycle of Given Points in a Polygonal Region

Biomolecular computing: Is it ready to take off?

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