Minimizing Profile of Graphs Using a Hybrid Simulating Annealing Algorithm

Kardam, Yogita Singh; Srivastava, Kamal; Sharma, R.

doi:10.1016/j.endm.2017.11.035

Cited by 1 publication

(2 citation statements)

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“…An adaptation of tabu search for bandwidth minimization problem (TS-BMP) and the two general-purpose optimizers are also used for comparison. Recently, a hybrid SA algorithm HSAPR is designed for this problem [22]. Besides the heuristic approaches, researchers from combinatorics community have attempted to find/prove exact optimal profiles of some classes of graphs [20,23,24].…”

Section: Existing Approachesmentioning

confidence: 99%

“…To examine how TSAPR works on a wide range of graphs, it is also applied to a subset of graphs from the Harwell-Boeing matrix collection. Table 4 shows the results obtained from the scatter search algorithm [3] and those obtained by HSAPR algorithm [22] on HB graphs. The results of the proposed TSAPR algorithm are shown in last column.…”

Section: Final Experimentsmentioning

confidence: 99%

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Tabu-Embedded Simulated Annealing Algorithm for Profile Minimization Problem

Kardam

Srivastava

2020

Computational Methods and Data Engineering

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Given an undirected connected graph G, the profile minimization problem (PMP) is to place the vertices of G in a linear layout (labeling) in such a way that the sum of profiles of the vertices in G is minimized, where the profile of a vertex is the difference of its labeling with the labeling of its left most neighbor in the layout. It is an NP-complete problem and has applications in various areas such as numerical analysis, fingerprinting, and information retrieval. In this paper, we design a tabuembedded simulated annealing algorithm for profile reduction (TSAPR) for PMP which uses a well-known spectral sequencing method to generate an initial solution. An efficient technique is employed to compute the profile of a neighbor of a solution. The experiments are conducted on different classes of graphs such as T 4 -trees, tensor product of graphs, complete bipartite graphs, triangulated triangle graphs, and a subset of Harwell-Boeing graphs. The computational results demonstrate an improvement in the existing results by TSAPR in most of the cases.

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