Virtual Topology Design for Minimizing Network Diameter and Average Hop Count in WDM Networks

We design virtual topologies in wavelength division multiplexing (WDM) networks to minimize the network diameter and average hop count, where network diameter refers to the number of hops of the longest shortest path and average hop count is the average number of hops among the shortest paths of all node pairs. Such objectives are important to WDM networks, especially to those with statistical multiplexing mechanisms such as optical burst switching (OBS) and optical packet switching (OPS). By minimizing the network diameter and average hop count, optical packets or bursts will experience less contention loss and smaller delay due to a reduced number of intermediate nodes en route. In this paper, we first formulate an integer linear program (ILP) for optimal design of virtual topologies with minimized network diameter and average hop count. Then, a novel heuristic least weight minimum diameter (LWMD) is proposed to find good solutions efficiently. Based on the virtual topology obtained, we further design two traffic accommodation schemes to provision wavelengths under a given traffic matrix, with guaranteed network diameter and minimized network resource consumption.published_or_final_versio

Near-Optimal Distributed Approximation of Minimum-Weight Connected Dominating Set

This paper presents a near-optimal distributed approximation algorithm for the minimum-weight connected dominating set (MCDS) problem. The presented algorithm finds an $O(\log n)$ approximation in $\tilde{O}(D+\sqrt{n})$ rounds, where $D$ is the network diameter and $n$ is the number of nodes. MCDS is a classical NP-hard problem and the achieved approximation factor $O(\log n)$ is known to be optimal up to a constant factor, unless P=NP. Furthermore, the $\tilde{O}(D+\sqrt{n})$ round complexity is known to be optimal modulo logarithmic factors (for any approximation), following [Das Sarma et al.---STOC'11].Comment: An extended abstract version of this result appears in the proceedings of 41st International Colloquium on Automata, Languages, and Programming (ICALP 2014

Log-Networks

We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows logarithmically with network size while the network diameter equals 2. We determine basic geometrical network properties, such as the size dependence of the number of links and the in- and out-degree distributions. We also compare our predictions with real networks where the node degree also grows slowly with time -- the Internet and the citation network of all Physical Review papers.Comment: 7 pages, 6 figures, 2-column revtex4 format. Version 2: minor changes in response to referee comments and to another proofreading; final version for PR

Void Traversal for Guaranteed Delivery in Geometric Routing

Geometric routing algorithms like GFG (GPSR) are lightweight, scalable algorithms that can be used to route in resource-constrained ad hoc wireless networks. However, such algorithms run on planar graphs only. To efficiently construct a planar graph, they require a unit-disk graph. To make the topology unit-disk, the maximum link length in the network has to be selected conservatively. In practical setting this leads to the designs where the node density is rather high. Moreover, the network diameter of a planar subgraph is greater than the original graph, which leads to longer routes. To remedy this problem, we propose a void traversal algorithm that works on arbitrary geometric graphs. We describe how to use this algorithm for geometric routing with guaranteed delivery and compare its performance with GFG