Compact representation of solution vectors in Kronecker-based Markovian analysis

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dc.citation.epage276en_US
dc.citation.spage260en_US
dc.contributor.authorBuchholz, P.en_US
dc.contributor.authorDayar, Tuğrulen_US
dc.contributor.authorKriege, J.en_US
dc.contributor.authorOrhan, M. Canen_US
dc.coverage.spatialQuebec City, Canada
dc.date.accessioned2018-04-12T11:42:15Z
dc.date.available2018-04-12T11:42:15Z
dc.date.issued2016-08en_US
dc.departmentDepartment of Computer Engineeringen_US
dc.descriptionDate of Conference: 23-25 August, 2016
dc.descriptionConference name: QEST: International Conference on Quantitative Evaluation of Systems - 13th International Conference, QEST 2016
dc.description.abstractIt is well known that the infinitesimal generator underlying a multi-dimensional Markov chain with a relatively large reachable state space can be represented compactly on a computer in the form of a block matrix in which each nonzero block is expressed as a sum of Kronecker products of smaller matrices. Nevertheless, solution vectors used in the analysis of such Kronecker-based Markovian representations still require memory proportional to the size of the reachable state space, and this becomes a bigger problem as the number of dimensions increases. The current paper shows that it is possible to use the hierarchical Tucker decomposition (HTD) to store the solution vectors during Kroneckerbased Markovian analysis relatively compactly and still carry out the basic operation of vector-matrix multiplication in Kronecker form relatively efficiently. Numerical experiments on two different problems of varying sizes indicate that larger memory savings are obtained with the HTD approach as the number of dimensions increases. © Springer International Publishing Switzerland 2016.en_US
dc.description.provenanceMade available in DSpace on 2018-04-12T11:42:15Z (GMT). No. of bitstreams: 1 bilkent-research-paper.pdf: 179475 bytes, checksum: ea0bedeb05ac9ccfb983c327e155f0c2 (MD5) Previous issue date: 2016en
dc.identifier.doi10.1007/978-3-319-43425-4_18en_US
dc.identifier.issn0302-9743
dc.identifier.urihttp://hdl.handle.net/11693/37502
dc.language.isoEnglishen_US
dc.publisherSpringeren_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/978-3-319-43425-4_18en_US
dc.source.titleQEST: International Conference on Quantitative Evaluation of Systems -13th International Conference, QEST 2016en_US
dc.subjectCompact vectorsen_US
dc.subjectHierarchical Tucker decompositionen_US
dc.subjectKronecker productsen_US
dc.subjectMarkov chainsen_US
dc.subjectReachable state spaceen_US
dc.subjectChainsen_US
dc.subjectMarkov processesen_US
dc.subjectMatrix algebraen_US
dc.subjectVectorsen_US
dc.subjectCompact representationen_US
dc.subjectInfinitesimal generatoren_US
dc.subjectKronecker producten_US
dc.subjectMarkovian representationen_US
dc.subjectMulti-dimensional Markov chainsen_US
dc.subjectNumerical experimentsen_US
dc.subjectTucker decompositionsen_US
dc.subjectVector-matrix multiplicationsen_US
dc.subjectVector spacesen_US
dc.titleCompact representation of solution vectors in Kronecker-based Markovian analysisen_US
dc.typeConference Paperen_US

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