42_01 - Design and Analysis of an MST-Based Topology...

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Design and Analysis of an MST-Based Topology Control Algorithm Ning Li, Jennifer C. Hou, and Lui Sha Department of Computer Science University of Illinois at Urbana-Champaign Urbana, IL 61801 { nli, jhou, lrs } @cs.uiuc.edu Abstract — In this paper, we present a Minimum Spanning Tree (MST) based topology control algorithm, called Local Minimum Spanning Tree (LMST), for wireless multi-hop networks. In this algorithm, each node builds its local minimum spanning tree independently and only keeps on-tree nodes that are one-hop away as its neighbors in the final topology. We analytically prove several important properties of LMST: (1) the topology derived under LMST preserves the network connectivity; (2) the node degree of any node in the resulting topology is bounded by 6; and (3) the topology can be transformed into one with bi-directional links (without impairing the network connectivity) after removal of all uni-directional links. These results are corroborated in the simulation study. I. INTRODUCTION Topology control and management – how to determine the transmission power of each node so as to maintain network connectivity while consuming the minimum possible power – has emerged to be one of the most important issues in wireless multi-hop networks [1]. Instead of transmitting using the max- imum possible power, nodes in a wireless multi-hop network collaboratively determine their transmission power and define the topology of the wireless network by the neighbor relation under certain criteria. This is in contrast to the “traditional” network in which each node transmits using its maximum transmission power and the topology is built implicitly by routing protocols (that update their routing caches as timely as possible) [2] [3] without considering the power issue. Not until recently has the issue of topology/power control with respect to maintaining network connectivity, optimizing network spatial reuse, and mitigating MAC-level interference attracted much attention. The importance of topology control lies in the fact that it critically affects the system performance in several ways. For one, as shown in [4], it affects network spatial reuse and hence the traffic carrying capacity. Choosing too large a power level results in excessive interference, while choosing too small a power level results in a disconnected network. Power control also effects the energy usage of communication, thus impacts on battery life, a critical resource in many mobile applications. In addition, topology control also impacts on contention for the medium. Collisions can be mitigated as much as possible by choosing the smallest transmission power subject to maintaining network connectivity [5] [6]. Several topology control algorithms [5], [7]–[9] have been proposed to create a power-efficient network topology in wireless multi-hop networks with limited mobility. We will summarize the existing work in Section II. Some of the algorithms require explicit propagation channel models (e.g., [9]), while others incur significant message exchanges (e.g.,
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42_01 - Design and Analysis of an MST-Based Topology...

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