Abstract
In this paper we describe an approximation algorihm for the vertex cover problem which has a worst case ratio Δ strictly smaller than 2 for graphs which don't have too many nodes (for example Δ≤1.9 if |V|≤1o13). Furthermore we present algorithms which improve in the case of degree bounded graphs the worst case ratios known up to now.
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R. Bar-Yehuda and S. Even: A linear-time approximation algorithm for the weighted vertex cover problem, J. Algorithms 2 (1982), 198–203
R. Bar-Yehuda and S. Even: On Approximating a Vertex Cover for Planar Graphs, Proc. 14th Annual ACM Symposium on Theory of Comuting (1982), 303–309
P. Erdös and T. Gallai: ON THE MINIMAL NUMBER OF VERTICES REPRESENTING THE EDGES OF A GRAPH, MAGYAR TUDOMÁNYOS AKADÉMIA MATEMATIKAI KUTATO INTÉZETÉNEK KÖZLEMÉNYEI VI. EVFOLYAM 1961, 181–203
S. Fajtlowicz: On the size of independent sets in graphs, Proc. 9th S.E. Conf. Combinatorics, Graph Theory and Computing (1978), 269–274
D. Hochbaum: Efficient Bounds for the Stable Set, Vertex Cover and Set Packing Problems, W.P. # 50-80-81, GSIA, Carnegie-Mellon University, May 1981
G. Hopkins and W. Staton: Girth and Independence Ratio, Canad. Math. Bull. 25 (1982), 179–186
J.E. Hopcroft and R.M. Karp: An n5/2 Algorithm for Maximal Matchings in Bipartite graphs, SIAM J. Comput. 4 (1973), 225–231
D. König: Theorie der endlichen und unendlichen Graphen, Leipzig, 1936
B. Monien: The Complexity of Determining a Shortest Cycle of even Length, Proc. Workshop "Graphtheoretic Concepts in Computer Science, Hanser Verlag, 1982
G.L. Nemhauser and L.E. Trotter: Vertex Packings: Structural Properties and Algorithms, Mathematical Programming 8 (1975), 232–248
E. Speckenmeyer: Covering all circuits in undirected graphs of degree 3 by a minimal number of vertices, Technical Report, Universität Paderborn, 1982
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© 1983 Springer-Verlag Berlin Heidelberg
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Monien, B., Speckenmeyer, E. (1983). Some further approximation algorithms for the vertex cover problem. In: Ausiello, G., Protasi, M. (eds) CAAP'83. CAAP 1983. Lecture Notes in Computer Science, vol 159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-12727-5_21
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DOI: https://doi.org/10.1007/3-540-12727-5_21
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