Abstract
The following issues in computational complexity remain imprecisely understood: the striking difference in the complexities of computing the permanent and determinant of a matrix despite their similar looking formulae, the complexity of checking if a directed graph contains an even length cycle, and the complexity of computing the number of perfect matchings in a graph using Pfaffian orientations. Via polynomial time equivalences, we show interrelationships among these issues.
Work done while visiting AT&T Bell Labs during 1986–87. Supported in part by a PYI Award, with matching funds from AT&T Bell Labs.
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© 1988 Springer-Verlag Berlin Heidelberg
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Vazirani, V.V., Yannakakis, M. (1988). Pfaffian orientations, 0/1 permanents, and even cycles in directed graphs. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_149
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DOI: https://doi.org/10.1007/3-540-19488-6_149
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