Localized Spanners for Wireless Networks

TL;DR

This paper introduces efficient localized algorithms for constructing sparse, low-weight, and planar spanners in wireless networks, optimizing for degree, weight, and planarity with minimal communication rounds.

Contribution

It presents novel localized algorithms for creating (1+e)-spanners with bounded degree and weight, and planar spanners with specific stretch factors, using only local information.

Findings

Constructed (1+e)-spanners with O(1) degree and weight O(w(MST))

Developed planar Cdel(1+e)(1+pi/2)-spanners with O(1) degree and weight O(w(MST))

Algorithms run in O(1) communication rounds, requiring nodes to know only their coordinates

Abstract

We present a new efficient localized algorithm to construct, for any given quasi-unit disk graph G=(V,E) and any e > 0, a (1+e)-spanner for G of maximum degree O(1) and total weight O(w(MST)), where w(MST) denotes the weight of a minimum spanning tree for V. We further show that similar localized techniques can be used to construct, for a given unit disk graph G = (V, E), a planar Cdel(1+e)(1+pi/2)-spanner for G of maximum degree O(1) and total weight O(w(MST)). Here Cdel denotes the stretch factor of the unit Delaunay triangulation for V. Both constructions can be completed in O(1) communication rounds, and require each node to know its own coordinates.