Heuristics for Network Coding in Wireless Networks

Multicast is a central challenge for emerging multi-hop wireless architectures such as wireless mesh networks, because of its substantial cost in terms of bandwidth. In this report, we study one specific case of multicast: broadcasting, sending data from one source to all nodes, in a multi-hop wireless network. The broadcast we focus on is based on network coding, a promising avenue for reducing cost; previous work of ours showed that the performance of network coding with simple heuristics is asymptotically optimal: each transmission is beneficial to nearly every receiver. This is for homogenous and large networks of the plan. But for small, sparse or for inhomogeneous networks, some additional heuristics are required. This report proposes such additional new heuristics (for selecting rates) for broadcasting with network coding. Our heuristics are intended to use only simple local topology information. We detail the logic of the heuristics, and with experimental results, we illustrate the behavior of the heuristics, and demonstrate their excellent performance

Local Approximation Schemes for Ad Hoc and Sensor Networks

We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs

Smaller Connected Dominating Sets in Ad Hoc and Sensor Networks based on Coverage by Two-Hop Neighbors

In this paper, we focus on the construction of an efficient dominating set in ad hoc and sensor networks. A set of nodes is said to be dominating if each node is either itself dominant or neighbor of a dominant node. This set can for example be used for broadcasting, so the smaller the set is, the more efficient it is. As a basis for our work, we use a heuristics given by Dai and Wu for constructing such a set and propose an enhanced definition to obtain smaller sets. This approach, in conjunction with the elimination of message overhead by Stojmenovic, has been shown (in recent studies) to be an excellent compromise with respect to a wide range of metrics considered. In our new definition, a node u is not dominant if there exists in its 2-hop neighborhood a connected set of nodes with higher priorities that covers u and its 1-hop neighbors. This new rule uses the exact same level of information required by the original heuristics, only neighbors of nodes and neighbors of neighbors must be known to apply it, but it takes advantage of some knowledge originally not taken into account: 1-hop neighbors can be covered by some 2-hop neighbors. We give the proof that the set obtained with this new definition is a subset of the one obtained with Dai and Wu's heuristics. We also give the proof that our set is always dominating for any graph, and connected for any connected graph. Two versions were considered: with topological and positional information, which differ in whether or not nodes are aware of links between their 2-hop neighbors that are not 1-hop neighbors. An algorithm for applying the concept at each node is described. We finally provide experimental data that demonstrates the superiority of our rule in obtaining smaller dominating sets. A centralized algorithm was used as a benchmark in the comparison. The overhead of the size of connected dominating set was reduced by about 15% with the topological variant and by about 30% with the positional variant of our new definition

An analysis of the lifetime of OLSR networks

The Optimized Link State Routing (OLSR) protocol is a well-known route discovery protocol for ad-hoc networks. OLSR optimizes the flooding of link state information through the network using multipoint relays (MPRs). Only nodes selected as MPRs are responsible for forwarding control traffic. Many research papers aim to optimize the selection of MPRs with a specific purpose in mind: e.g., to minimize their number, to keep paths with high Quality of Service or to maximize the network lifetime (the time until the first node runs out of energy). In such analyzes often the effects of the network structure on the MPR selection are not taken into account. In this paper we show that the structure of the network can have a large impact on the MPR selection. In highly regular structures (such as grids) there is even no variation in the MPR sets that result from various MPR selection mechanisms. Furthermore, we study the influence of the network structure on the network lifetime problem in a setting where at regular intervals messages are broadcasted using MPRs. We introduce the ’maximum forcedness ratio’, as a key parameter of the network to describe how much variation there is in the lifetime results of various MPR selection heuristics. Although we focus our attention to OLSR, being a widely implemented protocol, on a more abstract level our results describe the structure of connected sets dominating the 2-hop neighborhood of a node

An Order-based Algorithm for Minimum Dominating Set with Application in Graph Mining

Dominating set is a set of vertices of a graph such that all other vertices have a neighbour in the dominating set. We propose a new order-based randomised local search (RLS$_o$) algorithm to solve minimum dominating set problem in large graphs. Experimental evaluation is presented for multiple types of problem instances. These instances include unit disk graphs, which represent a model of wireless networks, random scale-free networks, as well as samples from two social networks and real-world graphs studied in network science. Our experiments indicate that RLS$_o$ performs better than both a classical greedy approximation algorithm and two metaheuristic algorithms based on ant colony optimisation and local search. The order-based algorithm is able to find small dominating sets for graphs with tens of thousands of vertices. In addition, we propose a multi-start variant of RLS$_o$ that is suitable for solving the minimum weight dominating set problem. The application of RLS$_o$ in graph mining is also briefly demonstrated

Applications and Routing Management of Wireless Sensor Networks

In this paper, we first describe some current and future applications of sensor networks. We present the conceptual framework of distributed routing strategies for wireless sensor networks. We show that under reasonable assumptions, this routing scheme guarantees ‘shortest path property’ which is quite desirable for sensor networks. We then discuss how this framework can be used to support distributed applications for sensor nodes acting as mobile devices. These schemes work well in low mobility conditions. We also discuss the performance of these heuristics