The distance approach to approximate combinatorial counting
dc.contributor.author | Barvinok, Alexander I. | en_US |
dc.contributor.author | Samorodnitsky, Alex | en_US |
dc.date.accessioned | 2006-09-08T19:41:49Z | |
dc.date.available | 2006-09-08T19:41:49Z | |
dc.date.issued | 2001-12 | en_US |
dc.identifier.citation | Barvinok, A.; Samorodnitsky, A.; (2001). "The distance approach to approximate combinatorial counting." Geometric and Functional Analysis 11(5): 871-899. <http://hdl.handle.net/2027.42/41843> | en_US |
dc.identifier.issn | 1016/443X | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/41843 | |
dc.description.abstract | We develop general methods to obtain fast (polynomial time) estimates of the cardinality of a combinatorially defined set via solving some randomly generated optimization problems on the set. Examples include enumeration of perfect matchings in a graph, linearly independent subsets of a set of vectors and colored spanning subgraphs of a graph. Geometrically, we estimate the cardinality of a subset of the Boolean cube via the average distance from a point in the cube to the subset with respect to some distance function. We derive asymptotically sharp cardinality bounds in the case of the Hamming distance and show that for small subsets a suitably defined “randomized” Hamming distance allows one to get tighter estimates of the cardinality. | en_US |
dc.format.extent | 315100 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Birkhäuser Verlag; Birkhäuser Verlag, Basel ; Springer Science+Business Media | en_US |
dc.subject.other | Legacy | en_US |
dc.title | The distance approach to approximate combinatorial counting | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA, e-mail: barvinok@math.lsa.umich.edu, US, | en_US |
dc.contributor.affiliationother | Institute for Advanced Study, Einstein Drive, Princeton, NJ 08540, USA, e-mail: asamor@ias.edu, US, | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/41843/1/39-11-5-871_10110871.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/s00039-001-8219-3 | en_US |
dc.identifier.source | Geometric and Functional Analysis | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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