Approximate Capacity Subregions of Uniform Multihop Wireless Networks

Abstract

Abstract-The capacity region of multihop wireless network is involved in many capacity optimization problems. However, the membership of the capacity region is NP-complete in general, and hence the direct application of capacity region is quite limited. As a compromise, we often substitute the capacity region with a polynomial approximate capacity subregion. In this paper, we construct polynomial μ-approximate capacity subregions of multihop wireless network under either 802.11 interference model or protocol interference model in which all nodes have uniform communication radii normalized to one and uniform interference radii ρ ≥ 1. The approximation factor μ decreases with ρ in general and is smaller than the best-known ones in the literature. For example, μ = 3 when ρ ≥ 2.2907 under the 802.11 interference model or when ρ ≥ 4.2462 under the protocol interference model. Our construction exploits a nature of the wireless interference called strip-wise transitivity of independence discovered in this paper and utilize the independence polytopes of cocomparability graphs in a spatial-divide-conquer manner. We also apply these polynomial μ-approximate capacity subregions to compute μ-approximate solutions for maximum (concurrent) multiflows.

Fast and simple approximation algorithms for maximum weighted independent set of links

“…Under the plane geometric variants of the protocol interference model with uniform interference radii, we further present a better approximation algorithm for MWISL which exploits the following strip-wise transitivity of independence discovered in [7]. Suppose that the maximum link length is normalized to one, and all nodes have an interference radius ≥ 1.…”

“…Division: The same division of given in [7] is adopted here. A representative of a link is defined to be its midpoint (respectively, sender) in the bidirectional (respectively, unidirectional) mode.…”

“…Then, each is still independent as argued in [7]. Among these independent sets for 0 ≤ < , the one with maximum weight is output by the algorithm StripWIS.…”

“…The value of was computed in [7]. In the bidirectional mode, The numeric values of can be computed with the quartic formula.…”

Multiflows in multi-channel multi-radio multihop wireless networks

“…On the other hand, polynomial approximation schemes (PTAS's) exist for maximum (concurrent) multiflow in a broad class of networks [13]. In addition to these hardness and approximation hardness results, a series of works have been devoted to practical approximation algorithms [1], [2], [4], [6], [8], [13], [15], [16]. Under either the 802.11 interference model with arbitrary interference and communication radii, the best known approximation bound is 23 [13].…”