TY - JOUR

T1 - Directed complete bipartite graph decompositions

T2 - Indirect constructions

AU - Dukes, Peter J.

AU - Colbourn, Charles

AU - Syrotiuk, Violet

N1 - Funding Information:
The research of V.R. Syrotiuk is supported in part by the National Science Foundation (NSF) under Grant ANI-0105985. Any opinions, findings, conclusions, or recommendations expressed are those of the authors and do not necessarily reflect the views of NSF.

PY - 2008/2/6

Y1 - 2008/2/6

N2 - Edge-decompositions of the complete λ-fold directed graph over(K, ⇒)n into (uniform) directed complete bipartite subgraphs over(K, ⇒)a, b form a model for wireless communication in sensor networks. Each node can be in one of three states: asleep (powered down), listening, or transmitting. Communication requires that the sender be transmitting, the destination listening, and no other node near the receiver transmitting. We represent nodes of the network as the vertices of over(K, ⇒)n, and time slots for communication as blocks of the graph decomposition. A block with out-vertices A and in-vertices B corresponds to a slot in which the nodes in A are transmitting, those in B are receiving, and all others are asleep. Thus, such a decomposition of λ over(K, ⇒)n guarantees that every ordered pair of nodes in the associated network can communicate in λ time slots. Additional constraints are needed to minimize interference by a third node. Some recursive constructions for these graph decompositions are established, with particular emphasis on properties minimizing interference.

AB - Edge-decompositions of the complete λ-fold directed graph over(K, ⇒)n into (uniform) directed complete bipartite subgraphs over(K, ⇒)a, b form a model for wireless communication in sensor networks. Each node can be in one of three states: asleep (powered down), listening, or transmitting. Communication requires that the sender be transmitting, the destination listening, and no other node near the receiver transmitting. We represent nodes of the network as the vertices of over(K, ⇒)n, and time slots for communication as blocks of the graph decomposition. A block with out-vertices A and in-vertices B corresponds to a slot in which the nodes in A are transmitting, those in B are receiving, and all others are asleep. Thus, such a decomposition of λ over(K, ⇒)n guarantees that every ordered pair of nodes in the associated network can communicate in λ time slots. Additional constraints are needed to minimize interference by a third node. Some recursive constructions for these graph decompositions are established, with particular emphasis on properties minimizing interference.

KW - Coverings

KW - Graph decompositions

KW - Graph designs

KW - Packings

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U2 - 10.1016/j.disc.2006.11.050

DO - 10.1016/j.disc.2006.11.050

M3 - Article

AN - SCOPUS:36248970733

VL - 308

SP - 367

EP - 374

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 2-3

ER -