### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 367-374 |

Number of pages | 8 |

Journal | Discrete Mathematics |

Volume | 308 |

Issue number | 2-3 |

DOIs | |

State | Published - Feb 6 2008 |

### Fingerprint

### Keywords

- Coverings
- Graph decompositions
- Graph designs
- Packings

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Discrete Mathematics*,

*308*(2-3), 367-374. https://doi.org/10.1016/j.disc.2006.11.050

**Directed complete bipartite graph decompositions : Indirect constructions.** / Dukes, Peter J.; Colbourn, Charles; Syrotiuk, Violet.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 308, no. 2-3, pp. 367-374. https://doi.org/10.1016/j.disc.2006.11.050

}

TY - JOUR

T1 - Directed complete bipartite graph decompositions

T2 - Indirect constructions

AU - Dukes, Peter J.

AU - Colbourn, Charles

AU - Syrotiuk, Violet

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

UR - http://www.scopus.com/inward/record.url?scp=36248970733&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36248970733&partnerID=8YFLogxK

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 -