On the construction of all shortest vertex-disjoint paths in Cayley graphs of abelian groups

doi:10.1016/J.TCS.2014.12.023

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On the construction of all shortest vertex-disjoint paths in Cayley graphs of abelian groups

Journal Article•DOI•

On the construction of all shortest vertex-disjoint paths in Cayley graphs of abelian groups

Cheng-Nan Lai¹•Institutions (1)

National Kaohsiung Marine University¹

16 Mar 2015-Theoretical Computer Science (Elsevier)-Vol. 571, pp 10-20

TL;DR: This paper gives a sufficient condition for the existence of m vertex-disjoint shortest paths from one source vertex to other m (not necessarily distinct) destination vertices in a Cayley graph of an abelian group, where m ?

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About: This article is published in Theoretical Computer Science.The article was published on 2015-03-16 and is currently open access. It has received 5 citations till now. The article focuses on the topics: Cayley graph & Floyd–Warshall algorithm.

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Journal Article•

Particle swarm optimisation algorithm for solving shortest path problems with mixed fuzzy arc weights

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Ali Ebrahimnejad¹, Zahra Karimnejad¹, Hamidreza Alrezaamiri¹•Institutions (1)

Islamic Azad University¹

02 Jun 2015-International Journal of Applied Decision Sciences

TL;DR: A particle swarm optimisation (PSO) algorithm in fuzzy environment is used for the shortest path problem on a network where arc weights are represented by different kinds of fuzzy numbers due to its superior convergence speed.

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Abstract: Shortest path problem is one of the most fundamental components in the fields of transportation and communication networks. This paper concentrates on a shortest path problem on a network where arc weights are represented by different kinds of fuzzy numbers. Recently, a genetic algorithm has been proposed for finding the shortest path in a network with mixed fuzzy arc weights due to the complexity of the addition of various fuzzy numbers for larger problems. In this paper, a particle swarm optimisation (PSO) algorithm in fuzzy environment is used for the same due to its superior convergence speed. The main contribution of this paper is the reduction of the time complexity of the existing genetic algorithm. Additionally, to compare the obtained results of the proposed PSO algorithm with those of the existing algorithm, two shortest path problems having mixed fuzzy arc weights are solved. The comparative examples illustrate that the algorithm proposed in this paper is more efficient than the existing algorithm in terms of time complexity.

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38 citations

Cites background from "On the construction of all shortest..."

...Shortest path (SP) problem is an important network structured linear programming problem that arises in several contexts and has deservedly received a great deal of attention in the literature (Aboutahoun, 2010; Rudniy et al., 2010; Chitra et al., 2011; Nikulin and Iftikhar, 2012; Dong et al., 2013; Olya 2014a, 2014b; Trevizan and Veloso, 2014; Lissovoi and Witt, 2015; Lai, 2015; Ardakani and Tavana, 2015; Grigoryan and Harutyunyan, 2015; Rezvanian and Meybodi, 2015; Aridhi et al., 2015)....
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...…2010; Rudniy et al., 2010; Chitra et al., 2011; Nikulin and Iftikhar, 2012; Dong et al., 2013; Olya 2014a, 2014b; Trevizan and Veloso, 2014; Lissovoi and Witt, 2015; Lai, 2015; Ardakani and Tavana, 2015; Grigoryan and Harutyunyan, 2015; Rezvanian and Meybodi, 2015; Aridhi et al., 2015)....
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Journal Article•DOI•

Sorting on graphs by adjacent swaps using permutation groups

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Dohan Kim

01 Nov 2016-Computer Science Review

TL;DR: This paper reviews the existing permutation sorting and permutation decomposition procedures for sorting on graphs with line, star, complete, and ring topologies by adjacent swaps and describes how abstract group-theoretical methods are used to find a minimum-length sequence of adjacent swaps needed to sort objects on those graphs.

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15 citations

Journal Article•DOI•

Low Time Complexity Algorithms for Path Computation in Cayley Graphs

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Daniela Aguirre-Guerrero¹, Guillaume Ducoffe², Lluís Fàbrega, Pere Vilà, David Coudert³ - Show less +1 more•Institutions (3)

Universidad Autónoma Metropolitana¹, University of Bucharest², French Institute for Research in Computer Science and Automation³

30 Apr 2019-Discrete Applied Mathematics

TL;DR: The proposed algorithms set a base in the design of adaptive and low-complexity routing schemes for networks whose interconnections are defined by CG and outperforms the state of art of topology-agnostic algorithms for disjoint shortest paths.

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3 citations

Cites background or methods from "On the construction of all shortest..."

...On the other hand, the algorithm for computing the K-shortest disjoint paths in CG of abelian groups runs in time O(K∆D) [12]....
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...algorithms for path computation in specific families of CG [12,14]....
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...An algorithm for computing the K-shortest vertex-disjoint paths in CG of abelian groups, which includes several families of CG such as hypercubes and buble-sort graphs, is presented in [12]....
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...Moreover, we show that for many families of CG used as model of communication networks, our algorithm for K-shortest disjoint paths stays competitive with respect to the algorithms presented in [12,18]....
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...In contrast to the algorithms presented in [12, 14, 16], our algorithms are topology-agnostic and have no constraints on the size of the computed paths....
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Journal Article•DOI•

On the construction of all shortest node-disjoint paths in star networks

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Cheng-Nan Lai¹•Institutions (1)

National Kaohsiung Marine University¹

01 Apr 2016-Information Processing Letters

TL;DR: A sufficient condition is given, which can be verified in O ( m n 1.5 ) time, for the existence of m node-disjoint shortest paths from one source node to other m (not necessarily distinct) target nodes, respectively, in an n-dimensional star network.

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2 citations

Journal Article•DOI•

Optimal node-disjoint paths in folded hypercubes

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Cheng-Nan Lai

01 Jan 2021-Journal of Parallel and Distributed Computing

TL;DR: This paper constructs m node-disjoint paths from one source node to other m (not necessarily distinct) target nodes in an n-dimensional folded hypercube so that both of their total length and maximal length are minimized, where m ≤ n+1.

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2 citations

References

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Book•

Graph theory with applications

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J. A. Bondy

01 Jan 1976

TL;DR: In this paper, the authors present Graph Theory with Applications: Graph theory with applications, a collection of applications of graph theory in the field of Operational Research and Management. Journal of the Operational research Society: Vol. 28, Volume 28, issue 1, pp. 237-238.

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Journal Article•DOI•

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Michael O. Rabin¹•Institutions (1)

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Abstract: An Information Dispersal Algorithm (IDA) is developed that breaks a file F of length L = u Fu into n pieces Fi, l ≤ i ≤ n, each of length uFiu = L/m, so that every m pieces suffice for reconstructing F. Dispersal and reconstruction are computationally efficient. The sum of the lengths uFiu is (n/m) · L. Since n/m can be chosen to be close to l, the IDA is space efficient. IDA has numerous applications to secure and reliable storage of information in computer networks and even on single disks, to fault-tolerant and efficient transmission of information in networks, and to communications between processors in parallel computers. For the latter problem provably time-efficient and highly fault-tolerant routing on the n-cube is achieved, using just constant size buffers.

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Topological properties of hypercubes

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Y. Saad¹, M.H. Schultz¹•Institutions (1)

Yale University¹

01 Jul 1988-IEEE Transactions on Computers

TL;DR: The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing and propose a theoretical characterization of the n-cube as a graph.

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Abstract: The n-dimensional hypercube is a highly concurrent loosely coupled multiprocessor based on the binary n-cube topology. Machines based on the hypercube topology have been advocated as ideal parallel architectures for their powerful interconnection features. The authors examine the hypercube from the graph-theory point of view and consider those features that make its connectivity so appealing. Among other things, they propose a theoretical characterization of the n-cube as a graph and and show how to map various other topologies into a hypercube. >

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1,302 citations