Computer Science ›› 2017, Vol. 44 ›› Issue (Z6): 129-132.doi: 10.11896/j.issn.1002-137X.2017.6A.029

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Linear-time Algorithm for Weighted Domination Problem of Strongly Chordal Graph Based on Local Ratio Method

ZHANG Xiu-jun, WU Pu, YANG Hong and SHAO Ze-hui   

  • Online:2017-12-01 Published:2018-12-01

Abstract: In an undirected graph G=(V,E),DV is dominating set if and only if any vertex v∈V-D adjacent to at least one vertex u∈D.The minimum weight dominating set problem consists of finding a dominating set of a graph G with minimum weight.By applying with the properties of strongly chordal graph,a linear-time algorithm based on local ratio method for the minimum weight dominating set problem on strongly chordal graph was proposed.We also provi-ded the proof of the time complexity of the proposed algorithm.

Key words: Local ratio method,Strongly chordal graph,Weighted dominating set,Linear time algorithm

[1] ROSE D J,TARJAN R E.Algorithmic Aspects of Vertex Elimination on Directed Graphs[J].Siam Journal on Computing,1975,34(1):245-254.
[2] FARBER M.Characterizations of strongly chordal graphs[J].Discrete Mathematics,1983,43(2/3):173-189.
[3] UEHARA R.Linear Time Algorithms on Chordal Bipartite and Strongly Chordal Graphs[M]∥Automata,Languages and Programming.Springer Berlin Heidelberg,2002:993-1004.
[4] FARBER M.Applications of LP duality to problems involving independence and domination[D].Rutgers University,1982.
[5] BOOTH K S,JOHNSON J H.Dominating sets in chordalgraphs[J].SIAM Journal on Computing,1982,11(1):191-199.
[6] FARBER M.Independent domination in chordal graphs[J].Ope-rations Research Letters,1982,1(4):134-138.
[7] BROIN M W,LOWE T J.A dynamic programming algorithm for covering problems with (greedy) totally balanced constraint matrices[J].SIAM Journal on Algebraic Discrete Methods,1986,7(3):348-357.
[8] CHANG G J.Labeling algorithms for domination problems insun-free chordal graphs[J].Discrete Applied Mathematics,1988,22(1):21-34.
[9] CHANG G J,NEMHAUSER G L.The k-domination and k-stability problems on sun-free chordal graphs[J].SIAM Journal on Algebraic Discrete Methods,1984,5(3):332-345.
[10] CHANG G J,NEMHAUSER G L.Covering,packing and genera-lized perfection[J].SIAM Journal on Algebraic Discrete Me-thods,1985,6(1):109-132.
[11] Farber M.Domination,independent domination,and duality in strongly chordal graphs[J].Discrete Applied Mathematics,1984,7(2):115-130.
[12] HOFFMAN A J,KOLEN A W J,Sakarovitch M.Totally-ba-lanced and greedy matrices[J].SIAM Journal on Algebraic Discrete Methods,1985,6(4):721-730.
[13] KRATSCH D.Finding dominating cliques efficiently,in strongly chordal graphs and undirected path graphs[J].Discrete Mathematics,1990,86(1-3):225-238.
[14] WIMER T V.Linear algorithms for the dominating cycle problems in series-parallel graphs,2-trees and Halin graphs[J].Congressus Numerantium,1987,56.
[15] GAREY M R,GRAHAM R L,ULLMAN J D.Worst-CaseAnalysis of Memory Allocation Algorithms[C]∥ACM Symposium on Theory of Computing.Denver,Colorado,USA,1972:93-94.
[16] GAREY M R,JOHNSON D S.Computers and Intractability:A Guide to the Theory of NP-Completeness[M].W.H.Freeman and Company Ltd,1979.
[17] ROSENKRANTZ D J,STEARNS R E,LEWIS P M.An analysis of several heuristics for thetraveling salesman problem[J].Siam Journal on Computing,1977,6(3):563-581.
[18] BAR-YEHUDA R,EVEN S.A linear-time approximation algorithm for the weighted vertex cover problem[J].Journal of Algorithms,1981,2(2):198-203.
[19] 堵丁柱.近似算法的设计与分析[M].北京:高等教育出版社,2011.

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