### Abstract

Multi-channel wireless networks are increasingly deployed as infrastructure networks, e.g. in metro areas. Network nodes frequently employ directional antennas to improve spatial throughput. In such networks, between two nodes, it is of interest to compute a path with a channel assignment for the links such that the path and link bandwidths are the same. This is achieved when any two consecutive links are assigned different channels, termed as "Channel-Discontinuity-Constraint" (CDC). CDC-paths are also useful in TDMA systems, where, preferably, consecutive links are assigned different time-slots. In the first part of this paper, we develop a t-spanner for CDC-paths using spatial properties; a sub-network containing O(n/θ) links, for any θ > 0, such that CDC-paths increase in cost by at most a factor t = (1 - 2 sin(θ/2))^{-2}. We propose a novel distributed algorithm to compute the spanner using an expected number of O(n log n) fixed-size messages. In the second part, we present a distributed algorithm to find minimum-cost CDC-paths between two nodes using O(n^{2}) fixed-size messages, by developing an extension of Edmonds' algorithm for minimum-cost perfect matching. In a centralized implementation, our algorithm runs in O(n^{2}) time improving the previous best algorithm which requires O(n^{3}) running time. Moreover, this running time improves to O(n/θ) when used in conjunction with the spanner developed.

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

Pages (from-to) | 153-169 |

Number of pages | 17 |

Journal | Ad Hoc Networks |

Volume | 13 |

Issue number | PART A |

DOIs | |

State | Published - Feb 2014 |

### Fingerprint

### Keywords

- Algorithms
- Directional antennas
- Routing
- Spanners

### ASJC Scopus subject areas

- Computer Networks and Communications
- Hardware and Architecture
- Software

### Cite this

*Ad Hoc Networks*,

*13*(PART A), 153-169. https://doi.org/10.1016/j.adhoc.2011.04.011

**On channel-discontinuity-constraint routing in wireless networks.** / Sankararaman, Swaminathan; Efrat, Alon; Ramasubramanian, Srinivasan; Agarwal, Pankaj K.

Research output: Contribution to journal › Article

*Ad Hoc Networks*, vol. 13, no. PART A, pp. 153-169. https://doi.org/10.1016/j.adhoc.2011.04.011

}

TY - JOUR

T1 - On channel-discontinuity-constraint routing in wireless networks

AU - Sankararaman, Swaminathan

AU - Efrat, Alon

AU - Ramasubramanian, Srinivasan

AU - Agarwal, Pankaj K.

PY - 2014/2

Y1 - 2014/2

N2 - Multi-channel wireless networks are increasingly deployed as infrastructure networks, e.g. in metro areas. Network nodes frequently employ directional antennas to improve spatial throughput. In such networks, between two nodes, it is of interest to compute a path with a channel assignment for the links such that the path and link bandwidths are the same. This is achieved when any two consecutive links are assigned different channels, termed as "Channel-Discontinuity-Constraint" (CDC). CDC-paths are also useful in TDMA systems, where, preferably, consecutive links are assigned different time-slots. In the first part of this paper, we develop a t-spanner for CDC-paths using spatial properties; a sub-network containing O(n/θ) links, for any θ > 0, such that CDC-paths increase in cost by at most a factor t = (1 - 2 sin(θ/2))-2. We propose a novel distributed algorithm to compute the spanner using an expected number of O(n log n) fixed-size messages. In the second part, we present a distributed algorithm to find minimum-cost CDC-paths between two nodes using O(n2) fixed-size messages, by developing an extension of Edmonds' algorithm for minimum-cost perfect matching. In a centralized implementation, our algorithm runs in O(n2) time improving the previous best algorithm which requires O(n3) running time. Moreover, this running time improves to O(n/θ) when used in conjunction with the spanner developed.

AB - Multi-channel wireless networks are increasingly deployed as infrastructure networks, e.g. in metro areas. Network nodes frequently employ directional antennas to improve spatial throughput. In such networks, between two nodes, it is of interest to compute a path with a channel assignment for the links such that the path and link bandwidths are the same. This is achieved when any two consecutive links are assigned different channels, termed as "Channel-Discontinuity-Constraint" (CDC). CDC-paths are also useful in TDMA systems, where, preferably, consecutive links are assigned different time-slots. In the first part of this paper, we develop a t-spanner for CDC-paths using spatial properties; a sub-network containing O(n/θ) links, for any θ > 0, such that CDC-paths increase in cost by at most a factor t = (1 - 2 sin(θ/2))-2. We propose a novel distributed algorithm to compute the spanner using an expected number of O(n log n) fixed-size messages. In the second part, we present a distributed algorithm to find minimum-cost CDC-paths between two nodes using O(n2) fixed-size messages, by developing an extension of Edmonds' algorithm for minimum-cost perfect matching. In a centralized implementation, our algorithm runs in O(n2) time improving the previous best algorithm which requires O(n3) running time. Moreover, this running time improves to O(n/θ) when used in conjunction with the spanner developed.

KW - Algorithms

KW - Directional antennas

KW - Routing

KW - Spanners

UR - http://www.scopus.com/inward/record.url?scp=84888869687&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888869687&partnerID=8YFLogxK

U2 - 10.1016/j.adhoc.2011.04.011

DO - 10.1016/j.adhoc.2011.04.011

M3 - Article

AN - SCOPUS:84888869687

VL - 13

SP - 153

EP - 169

JO - Ad Hoc Networks

JF - Ad Hoc Networks

SN - 1570-8705

IS - PART A

ER -