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Abstract
We study a constrained version of the knapsack problem in which dependencies between items are given by the adjacencies of a graph. In the1-neighbour knapsack problem, an item can be selected only if at least one of its neighbours is also selected. We give approximation algorithms and hardness results when the nodes have both uniform and arbitrary weight and profit functions, and when the dependency graph is directed and undirected.
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References
Boland, N., Fricke, C., Froyland, G., Sotirov, R.: Clique-based facets for the precedence constrained knapsack problem. Technical report. Tilburg University Repository, Netherlands (2005),http://arno.uvt.nl/oai/wo.uvt.nl.cgi
Borradaile, G., Heeringa, B., Wilfong, G.: The knapsack problem with neighbour constraints. CoRR, abs/0910.0777 (2011)
Feige, U.: A threshold of lnn for approximating set cover. J. ACM 45(4), 634–652 (1998)
Goundan, P.R., Schulz, A.S.: Revisiting the greedy approach to submodular set function maximization (2009) (preprint)
Halperin, E., Krauthgamer, R.: Polylogarithmic inapproximability. In: Proceedings of STOC, pp. 585–594 (2003)
Ibarra, O.H., Kim, C.E.: Fast approximation algorithms for the knapsack and sum of subset problems. J. ACM 22, 463–468 (1975)
Johnson, D.S., Niemi, K.A.: On knapsacks, partitions, and a new dynamic programming technique for trees. Mathematics of Operations Research, 1–14 (1983)
Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Heidelberg (2004)
Khuller, S., Moss, A., Naor(Seffi), J.: The budgeted maximum coverage problem. Inf. Process. Lett. 70(1), 39–45 (1999)
Kolliopoulos, S.G., Steiner, G.: Partially ordered knapsack and applications to scheduling. Discrete Applied Mathematics 155(8), 889–897 (2007)
Kulik, A., Shachnai, H., Tamir, T.: Maximizing submodular set functions subject to multiple linear constraints. In: Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2009, pp. 545–554. Society for Industrial and Applied Mathematics, Philadelphia (2009)
Lee, J., Mirrokni, V.S., Nagarajan, V., Sviridenko, M.: Non-monotone submodular maximization under matroid and knapsack constraints. In: Proceedings of the 41st Annual ACM Symposium on Theory of Computing, STOC 2009, pp. 323–332. ACM, New York (2009)
Sviridenko, M.: A note on maximizing a submodular set function subject to a knapsack constraint. Operations Research Letters 32(1), 41–43 (2004)
Vazirani, V.: Approximation Algorithms. Springer, Berlin (2001)
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Authors and Affiliations
Oregon State University, United States
Glencora Borradaile
Williams College, United Kingdom
Brent Heeringa
Bell Labs, United States
Gordon Wilfong
- Glencora Borradaile
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- Brent Heeringa
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- Gordon Wilfong
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Editors and Affiliations
Digital Ecosystems & Business Intelligence Institute, Curtin University, Perth, Australia
Costas S. Iliopoulos
Department of Computing and Software Information Technology Building, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada
William F. Smyth
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Borradaile, G., Heeringa, B., Wilfong, G. (2011). The 1-Neighbour Knapsack Problem. In: Iliopoulos, C.S., Smyth, W.F. (eds) Combinatorial Algorithms. IWOCA 2011. Lecture Notes in Computer Science, vol 7056. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25011-8_6
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