Abstract
We consider two generic problems of combinatorial search under the additive model. The first one is the problem of reconstructing bounded-weight vectors. We establish an optimal upper bound and observe that it unifies many known results for coin-weighing problems. The developed technique provides a basis for the graph reconstruction problem. Optimal upper bound is proved for the class of k-degenerate graphs.
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References
Alok Aggarwal, Don Coppersmith, and Dan Kleitman. A generalized model for understanding evasiveness. Information Processing Letters, 30:205–208, 1989.
Martin Aigner. Combinatorial Search. John Wiley & Sons, 1988.
Noga Alon. Separating matrices. private communication, May 1997.
Noga Alon and Joel Spencer. The Probabilistic Method. John Wiley & Sons, 1992.
Béla Bollobás. Extremal Graph Theory. Academic Press, 1978.
Ding-Zhu Du and Frank K. Hwang. Combinatorial Group Testing and its applications, volume 3 of Series on applied mathematics. World Scientific, 1993.
Paul Erdős and Joel Spencer. Probabilistic Methods in Combinatorics. 1974.
Vladimir Grebinski and Gregory Kucherov. Optimal query bounds for reconstructing a hamiltonian cycle in complete graphs. In Proceedings of the 5th Israeli Symposium on Theory of Computing and Systems, pages 166–173. IEEE Press, 1997.
Vladimir Grebinski and Gregory Kucherov. Optimal reconstruction of graphs under the additive model. In Rainer Burkard and Gerhard Woeginger, editors, Algorithms — ESA’97, volume 1284 of LNCS, pages 246–258. Springer, 1997.
Bernt Lindström. On Möbius functions and a problem in combinatorial number theory. Canad. Math. Bull., 14(4):513–516, 1971.
Bernt Lindström. Determining subsets by unramified experiments. In J.N. Srivastava, editor, A Survey of Statistical Designs and Linear Models, pages 407–418. North Holland, Amsterdam, 1975.
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© 1998 Springer-Verlag Berlin Heidelberg
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Grebinski, V. (1998). On the Power of Additive Combinatorial Search Model. In: Hsu, WL., Kao, MY. (eds) Computing and Combinatorics. COCOON 1998. Lecture Notes in Computer Science, vol 1449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68535-9_23
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DOI: https://doi.org/10.1007/3-540-68535-9_23
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