r-shrink: a heuristic for improving minimum power broadcast trees in wireless networks

Abstract

Abstract-Broadcasting in wireless networks, unlike wired networks, inherently reaches several nodes with a single transmission. For omni-directional wireless broadcast to a node, all nodes closer will also be reached. This property can be used to compute routing trees which minimize the sum of the transmitter powers. It has been shown that this problem is NP-complete. In this paper, we present the r-shrink procedure, a heuristic for improving the solutions obtained using fast sub-optimal algorithms. Specifically, we focus on the lowcomplexity BIP algorithm and Prim's minimum spanning tree algorithm and show through extensive simulations that better solutions are obtained almost always, with considerably lower tree power, if the proposed procedure is used to improve the trees generated using these algorithms.

A Two-Phase Constructive Heuristic for Minimum Energy Broadcasting in Wireless Ad Hoc Networks

“…Sweep [9], Iterative Maximum-Branch Minimization (IMBM) [26], Embedded Wireless Multicast Advantage (EWMA) [4], Broadcast Incremental-Decremental Power (BIDP) [27], and Shrinking Overlapped Range (SOR) [28] are some typical examples of tree based algorithms where a tree is updated to a new tree at each improvement step by removing some of the links of the previous one and adding new links. The power assignment based algorithms like r-shrink [29] and Largest Expanding Sweep Search (LESS) [30] make moves based on a new power assignment for each node in the network.…”

Iterated Local Optimization for Minimum Energy Broadcast

“…The underlying philosophy of our current work is exactly the opposite of the Iterative Maximum Branch Minimization (IMBM) [17] and r-shrink [6] algorithms. As suggested by the names of these algorithms, "range reduction" is emphasized, meaning that the maximum branch (edge) and the corresponding range of each node is progressively broken into smaller pieces (i.e., into multihop edges or ranges).…”

“…(a) Without range expansion in N H ess , inspecting gain for current range assignment is no different from the post sweep algorithm [26]. (b) The neighborhoods used in Iterative Maximum Branch Minimization (IMBM) [17] and r-shrink algorithms [6] are obtained by updating a node's parent to a node which is not one of its descendants. Clearly, this is a special case of N H ee when v = v .…”

“…algorithms that may be considered as local search algorithms in a broader sense, including Post Sweep procedure [26], Iterative Maximum Branch Minimization (IMBM) [17], r-Shrink [6], although not specifically stated as such. Interpreting these algorithms as local search facilitates analysis of advantages or disadvantages therein, and after the underlying concepts of each algorithm are distilled as local search, we can easily extend the concepts to devise better performing heuristics.…”

“…Over the past years, several (greedy) construction heuristics have been developed such that a feasible solution is built from scratch, say, using locations of nodes as input. Some of the representative algorithms in this category are: the Broadcast Incremental Power (BIP) [26], Embedded Wireless Multicast Advantage (EWMA) [3], Broadcast Average Incremental Power (BAIP) [24], Greedy Perimeter Broadcast Efficiency (GPBE) [13], Center Oriented Broadcast Routing Algorithm (COBRA) [16], Steiner tree based heuristics by Liang [18], Ant Colony System (ACS) based approach [6], and G-Remit [25], etc.…”