Abstract
We present a randomized \(\left({89\over169}-\epsilon\right)\)-approximation algorithm for the weighted maximum triangle packing problem, for any given ε> 0. This is the first algorithm for this problem whose performance guarantee is better than \({1\over2}\). The algorithm also improves the best known approximation bound for the maximum 2-edge path packing problem.
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References
Arkin, E., Hassin, R.: On local search for weighted packing problems. Mathematics of Operations Research 23, 640–648 (1998)
Bafna, V., Narayanan, B., Ravi, R.: Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles). Discrete Applied Mathematics 71, 41–53 (1996)
Berman, P.: A d/2 approximation for maximum weight independent set in d-claw free graphs. Nordic Journal of Computing 7, 178–184 (2000)
Chandra, B., Halldórsson, M.M.: Greedy local improvement and weighted set packing approximation. Journal of Algorithms 39, 223–240 (2001)
Chlebík, M., Chlebíková, J.: Approximating hardness for small occurrence instances of NP-hard problems. In: Petreschi, R., Persiano, G., Silvestri, R. (eds.) CIAC 2003. LNCS, vol. 2653, pp. 152–164. Springer, Heidelberg (2003)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman, New York (1978)
Halldórsson, M.M.: Approximating discrete collections via local improvements. In: Proceedings of the Sixth SODA 95.Annual ACM-SIAM Symposium on Discrete Algorithms SODA 1995, pp. 160–169 (1995)
Hartvigsen, D.: Extensions of Matching Theory. Ph.D. Thesis, Carnegie-Mellon University (1984)
Hassin, R., Rubinstein, S.: Better approximations for Max TSP. Information Processing Letters 75, 181–186 (2000)
Hassin, R., Rubinstein, S.: An approximation algorithm for maximum packing of 3-edge paths. Information Processing Letters 63, 63–67 (1997)
Hurkens, C.A.J., Schrijver, A.: On the size of systems of sets every t of which have an SDR, with an application to the worst-case ratio of heuristics for packing problems. SIAM J. on Discrete Mathematics 2, 68–72 (1989)
Kann, V.: Maximum bounded 3-dimensional matching is MAX SNP-complete. Information processing Letters 37, 27–35 (1991)
Korte, B., Hausmann, D.: An analysis of the greedy heuristic for independence systems. Annals of Discrete Mathematics 2, 65–74 (1978)
Pekny, J.F., Miller, D.L.: A staged primal-dual algorithm for finding a minimum cost perfect two-matching in an undirected graph. ORSA Journal on Computing 6, 68–81 (1994)
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Hassin, R., Rubinstein, S. (2004). An Approximation Algorithm for Maximum Triangle Packing. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_37
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DOI: https://doi.org/10.1007/978-3-540-30140-0_37
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