#### Path cover problems on bipartite interconnection networks = 이분 상호연결망에서의 경로 커버 문제

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dc.contributor.authorJo, Shin-Haeng-
dc.contributor.author조신행-
dc.date.accessioned2013-09-12T01:46:38Z-
dc.date.available2013-09-12T01:46:38Z-
dc.date.issued2013-
dc.identifier.urihttp://library.kaist.ac.kr/search/detail/view.do?bibCtrlNo=513954&flag=dissertation-
dc.identifier.urihttp://hdl.handle.net/10203/180370-
dc.description학위논문(박사) - 한국과학기술원 : 전산학과, 2013.2, [ v, 53 p. ]-
dc.description.abstractA \emph{paired many-to-many $k$-disjoint path cover} (\emph{$k$-DPC} for short) of a graph is a set of $k$ disjoint paths joining $k$ disjoint source-sink pairs that cover all the vertices of the graph. Extending the notion of DPC, we define a {\em paired many-to-many bipartite $k$-DPC} (\emph{$k$-BiDPC}) of a bipartite graph $G$ to be a set of $k$ disjoint paths joining $k$ distinct source-sink pairs that altogether cover the same number of vertices as the maximum number of vertices covered when the source-sink pairs are given in the complete bipartite, spanning supergraph of $G$. We consider the problem of finding paired many-to-many $2$-DPC and paired many-to-many $1$-BiDPC in an $m$-dimensional bipartite HL-graph and the problem of finding paired many-to-many $k$-BiDPC in an $m$-dimensional hypercube. It is proved that every $m$-dimensional bipartite HL-graph, under the condition that at most $m-3$ faulty edges removed, has a paired many-to-many $2$-DPC if the set of sources and sinks is balanced in the sense that it contains the same number of vertices from each part of the bipartition, where $m\geq 4$. Furthermore, every $m$-dimensional bipartite HL-graph, where $m\geq 4$, has a paired many-to-many 2-DPC in which the two paths have the same length if each source-sink pair is balanced in that source and sink do not have the same color. Using the $2$-DPC properties, it is proved that every $m$-dimensional bipartite HL-graph, under the condition that either at most $m-2$ faulty edges, or one faulty vertex and at most $m-3$ faulty edges removed has a paired many-to-many $1$-BiDPC, where $m\geq 3$. Using this result, we show that every $m$-dimensional hypercube, $Q_m$, under the condition that $f$ or less faulty elements (vertices and/or edges) are removed, has a paired many-to-many $k$-BiDPC joining $k$ distinct source-sink pairs for any $f$ and $k\geq 1$ subject to $f+2k\leq m$. This implies that $Q_m$ with $m-2$ or less faulty elements is strongly Hamilto...eng
dc.languageeng-
dc.publisher한국과학기술원-
dc.subjectdisjoint path cover-
dc.subjecthypercube-
dc.subjecthypercube-like graphs-
dc.subjectgraph theory-
dc.subject서로 소인 경로 커버-
dc.subject하이퍼큐브-
dc.subject유사 하이퍼큐브 그래프-
dc.subject고장 감내-
dc.subject그래프 이론-
dc.subjectfault-tolerance-
dc.titlePath cover problems on bipartite interconnection networks = 이분 상호연결망에서의 경로 커버 문제-
dc.typeThesis(Ph.D)-
dc.identifier.CNRN513954/325007 -
dc.description.department한국과학기술원 : 전산학과, -
dc.identifier.uid020047581-
dc.contributor.localauthorShin, Sung-Yong-
dc.contributor.localauthor신성용-
dc.contributor.localauthorChwa, Kyung-Yong-
dc.contributor.localauthor좌경룡-
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CS-Theses_Ph.D.(박사논문)
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