Abstract
The maximal matching problem, i.e., the computation of a matching that is not a proper subset of another matching, is a fundamental optimization problem and algorithms for maximal matchings have been used as submodules for problems like maximal node-disjoint paths or maximum flow. Since in some applications graphs become larger and larger, a research branch has emerged which is concerned with the design and analysis of implicit algorithms for classical graph problems. Input graphs are given as characteristic Boolean functions of their edge sets and problems have to be solved by functional operations. As OBDDs, which are closely related to deterministic finite automata, are a well-known data structure for Boolean functions, OBDD-based algorithms are used as a heuristic approach to handle very large graphs. Here, an implicit OBDD-based maximal matching algorithm is presented that uses only a polylogarithmic number of functional operations with respect to the number of vertices of the input graph.
The first author has been supported by DFG project BO 2755/1-1.
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References
Bollig, B.: Exponential space complexity for OBDD-based reachability analysis. Information Processing Letters 110, 924–927 (2010)
Bollig, B.: Exponential Space Complexity for Symbolic Maximum Flow Algorithms in 0-1 Networks. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 186–197. Springer, Heidelberg (2010)
Bollig, B.: On Symbolic OBDD-Based Algorithms for the Minimum Spanning Tree Problem. In: Wu, W., Daescu, O. (eds.) COCOA 2010, Part II. LNCS, vol. 6509, pp. 16–30. Springer, Heidelberg (2010)
Bollig, B., Pröger, T.: An efficient implicit OBDD-based algorithm for maximal matchings (2011), http://ls2-www.cs.tu-dortmund.de/~bollig/maxMatching.pdf
Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Computers 35(8), 677–691 (1986)
Gentilini, R., Piazza, C., Policriti, A.: Computing strongly connected components in a linear number of symbolic steps. In: Proc. of SODA, pp. 573–582 (2003)
Gentilini, R., Piazza, C., Policriti, A.: Symbolic graphs: linear solutions to connectivity related problems. Algorithmica 50(1), 120–158 (2008)
Goldberg, A.V., Plotkin, S.K., Vaidya, P.M.: Sublinear time parallel algorithms for matching and related problems. Journal of Algorithms 14(2), 180–213 (1993)
Hachtel, G.D., Somenzi, F.: A symbolic algorithm for maximum flow in 0 − 1 networks. Formal Methods in System Design 10, 207–219 (1997)
Jájá, J.: An introduction to parallel algorithms. Addison-Wesley Publishing Company (1992)
Kelsen, P.: An optimal parallel algorithm for maximal matching. Information Processing Letters 52(4), 223–228 (1994)
Sawitzki, D.: Implicit Flow Maximization by Iterative Squaring. In: Van Emde Boas, P., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2004. LNCS, vol. 2932, pp. 301–313. Springer, Heidelberg (2004)
Sawitzki, D.: The Complexity of Problems on Implicitly Represented Inputs. In: Wiedermann, J., Tel, G., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2006. LNCS, vol. 3831, pp. 471–482. Springer, Heidelberg (2006)
Sawitzki, D.: Implicit simulation of FNC algorithms. Tech. Rep. TR07-028, ECCC Report (2007)
Wegener, I.: Branching programs and binary decision diagrams: theory and applications. SIAM (2000)
Woelfel, P.: Symbolic topological sorting with OBDDs. J. Discrete Algorithms 4(1), 51–71 (2006)
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Bollig, B., Pröger, T. (2012). An Efficient Implicit OBDD-Based Algorithm for Maximal Matchings. In: Dediu, AH., Martín-Vide, C. (eds) Language and Automata Theory and Applications. LATA 2012. Lecture Notes in Computer Science, vol 7183. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28332-1_13
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DOI: https://doi.org/10.1007/978-3-642-28332-1_13
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