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Minimal contention-free matrices with application to multicasting
dc.contributor.author | Cohen, Johanne |
dc.contributor.author | Fraigniaud, Pierre |
dc.contributor.author | Mitjana Riera, Margarida |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I |
dc.date.accessioned | 2007-04-30T08:40:19Z |
dc.date.available | 2007-04-30T08:40:19Z |
dc.date.created | 2000 |
dc.date.issued | 2000 |
dc.identifier.citation | Cohen, Johanne; Fraigniaud, Pierre; Mitjana Riera, Margarida. “Minimal contention-free matrices with application to multicasting”. A: DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 1998, vol. 53, núm , p. 17-33. |
dc.identifier.uri | http://hdl.handle.net/2117/804 |
dc.description.abstract | In this paper, we show that the multicast problem in trees can be expressed in term of arranging rows and columns of boolean matrices. Given a $p \times q$ matrix $M$ with 0-1 entries, the {\em shadow} of $M$ is defined as a boolean vector $x$ of $q$ entries such that $x_i=0$ if and only if there is no 1-entry in the $i$th column of $M$, and $x_i=1$ otherwise. (The shadow $x$ can also be seen as the binary expression of the integer $x=\sum_{i=1}^{q}x_i 2^{q-i}$. Similarly, every row of $M$ can be seen as the binary expression of an integer.) According to this formalism, the key for solving a multicast problem in trees is shown to be the following. Given a $p \times q$ matrix $M$ with 0-1 entries, finding a matrix $M^*$ such that: 1- $M^*$ has at most one 1-entry per column; 2- every row $r$ of $M^*$ (viewed as the binary expression of an integer) is larger than the corresponding row $r$ of $M$, $1 \leq r \leq p$; and 3- the shadow of $M^*$ (viewed as an integer) is minimum. We show that there is an $O(q(p+q))$ algorithm that returns $M^*$ for any $p \times q$ boolean matrix $M$. The application of this result is the following: Given a {\em directed} tree $T$ whose arcs are oriented from the root toward the leaves, and a subset of nodes $D$, there exists a polynomial-time algorithm that computes an optimal multicast protocol from the root to all nodes of $D$ in the all-port line model. |
dc.format.extent | 17 p. |
dc.language.iso | eng |
dc.subject.lcsh | Information and Communication Applications, Inc. |
dc.subject.lcsh | Operations research |
dc.subject.lcsh | Computer systems |
dc.subject.lcsh | Graph theory |
dc.subject.other | Application to Multicasting |
dc.subject.other | Minimal Contention-free Matrices |
dc.title | Minimal contention-free matrices with application to multicasting |
dc.type | Article |
dc.subject.lemac | Investigació operativa |
dc.subject.lemac | Arquitectura de computadors |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::68 Computer science::68M Computer system organization |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.subject.ams | Classificació AMS::90 Operations research, mathematical programming::90B Operations research and management science |
dc.subject.ams | Classificació AMS::94 Information And Communication, Circuits::94A Communication, information |
dc.rights.access | Open Access |
local.personalitzacitacio | true |
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