On the connection between interval size functions and path counting

Bampas, E; Gobel, AN; Pagourtzis, A; Tentes, A

dc.contributor.author	Bampas, E	en
dc.contributor.author	Gobel, AN	en
dc.contributor.author	Pagourtzis, A	en
dc.contributor.author	Tentes, A	en
dc.date.accessioned	2014-03-01T02:46:16Z
dc.date.available	2014-03-01T02:46:16Z
dc.date.issued	2009	en
dc.identifier.issn	03029743	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/32630
dc.subject	Perfect Match	en
dc.subject.other	Counting class	en
dc.subject.other	Counting problems	en
dc.subject.other	Decision version	en
dc.subject.other	Interval size	en
dc.subject.other	New class	en
dc.subject.other	P-complete problem	en
dc.subject.other	Perfect matchings	en
dc.subject.other	Size separation	en
dc.title	On the connection between interval size functions and path counting	en
heal.type	conferenceItem	en
heal.identifier.primary	10.1007/978-3-642-02017-9_14	en
heal.identifier.secondary	http://dx.doi.org/10.1007/978-3-642-02017-9_14	en
heal.publicationDate	2009	en
heal.abstract	We investigate the complexity of hard counting problems that belong to the class #P but have easy decision version; several wellknown problems such as #Perfect Matchings, #DNFSat share this property. We focus on classes of such problems which emerged through two disparate approaches: one taken by Hemaspaandra et al. [1] who defined classes of functions that count the size of intervals of ordered strings, and one followed by Kiayias et al. [2] who defined the class TotP, consisting of functions that count the total number of paths of NP computations. We provide inclusion and separation relations between TotP and interval size counting classes, by means of new classes that we define in this work. Our results imply that many known #P-complete problems with easy decision are contained in the classes defined in [1]-but are unlikely to be complete for these classes under certain types of reductions. We also define a new class of interval size functions which strictly contains FP and is strictly contained in TotP under reasonable complexity-theoretic assumptions. We show that this new class contains some hard counting problems. © Springer-Verlag Berlin Heidelberg 2009.	en
heal.journalName	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)	en
dc.identifier.doi	10.1007/978-3-642-02017-9_14	en
dc.identifier.volume	5532 LNCS	en
dc.identifier.spage	108	en
dc.identifier.epage	117	en