Abstract — We propose two new distributed scheduling policies for ad hoc wireless networks that can achieve provable capacity regions. Known scheduling policies that guarantee comparable capacity regions are either centralized or need computation time that increases with the size of the network. In contrast, the unique feature of the proposed distributed scheduling policies is that they are constant-time policies, i.e., the time needed for computing a schedule is independent of the network size. Hence, they can be easily deployed in large networks. I.

Abstract — The capacity of ad hoc wireless networks can be substantially increased by equipping each network node with multiple radio interfaces that can operate on multiple non-overlapping channels. However, new scheduling, channelassignment, and routing algorithms are required to fully utilize the increased bandwidth in multi-channel multi-radio ad hoc networks. In this paper, we develop a fully distributed algorithm that jointly solves the channel-assignment, scheduling and routing problem. Our algorithm is an online algorithm, i.e., it does not require prior information on the offered load to the network, and can adapt automatically to the changes in the network topology and offered load. We show that our algorithm is provably efficient. That is, even compared with the optimal centralized and offline algorithm, our proposed distributed algorithm can achieve a provable fraction of the maximum system capacity. Further, the achievable fraction that we can guarantee is larger than that of some other comparable algorithms in the literature. I.

In this paper, we present fast and fully distributed algorithms for matching in weighted trees and general weighted graphs. The time complexity as well as the approximation ratio of the tree algorithm is constant. In particular, the approximation ratio is 4. For the general graph algorithm we prove a constant ratio bound of 5 and a polylogarithmic time complexity of O(log n).

Abstract. We present a distributed approximation algorithm that computes in every graph G a matching M of size at least 2 β(G), where 3 β(G) is the size of a maximum matching in G. The algorithm runs in O(log 4 |V (G)|) rounds in the synchronous, message passing model of computation and matches the best known asymptotic complexity for computing a maximal matching in the same protocol. This improves the running time of an algorithm proposed recently by the authors in [2]. 1

) Micha/l Ha'n'ckowiak Dept of Math and CS Adam Mickiewicz University Pozna'n, Poland Micha/l Karo'nski Dept of Math and CS Adam Mickiewicz University Pozna'n, Poland & Dept of Math and CS Emory University Atlanta, Georgia, USA Alessandro Panconesi Dept of CS University of Bologna Bologna, Italy Abstract We show that maximal matchings can be computed deterministically in O(log 4 n) rounds in the synchronous, message-passing model of computation. This improves on an earlier result by three log-factors. 1 Introduction In this paper we show that maximal matchings (MM's) can be computed deterministically in O(log 4 n) rounds in the synchronous, message-passing model of computation. This improves substantially on an earlier result by the present authors, which shows that MM's can be computed in O(log 7 n) many rounds [9]. This rather substantial improvement in asymptotics is based on several new algorithmic ideas that, we hope, might prove useful in other conte...

It has been an important research topic since 1992 to maximize stability region in constrained queueing systems, which includes the study of scheduling over wireless ad hoc networks. In this paper, we propose a framework to study a wide range of existing and future scheduling algorithms and characterize the achieved tradeoffs in stability, delay, and complexity. These characterizations reveal interesting properties hidden in the study of any one or two dimensions in isolation. For example, decreasing complexity from exponential to polynomial, while keeping stability region the same, generally comes at the expense of exponential growth of delays. Investigating trade-offs in the 3-dimensional space allows a designer to fix one dimension and vary the other two jointly. For example, incentives for using scheduling algorithms with only partial throughput-guarantee can be quantified with regards to delay and complexity. Tradeoff analysis is then extended to systems with congestion control through utility maximization for non-stabilizable arrival inputs, where the complexity-utility-delay trade-off is shown to be different from the complexity-stability-delay tradeoff. Finally, we analyze more practical models with bounded message size, and consider “effective throughput” which reflects resource occupied by control messages. We show that effective throughput may degrade significantly in certain scheduling algorithms, and suggest a mechanism to avoid this problem in light of the 3D tradeoff framework.

In this paper we consider the problem of computing a minimum-weight vertex-cover in an n-node, weighted, undirected graph G = (V,E). We present a fully distributed algorithm for computing vertex covers of weight at most twice the optimum, in the case of integer weights. Our algorithm runs in an expected number of O(logn + log ˆW) communication rounds, where ˆW is the average vertex-weight. The previous best algorithm for this problem requires O(logn(log n + log ˆW)) rounds and it is not fully distributed. For a maximal matching M in G it is a well-known fact that any vertex-cover in G needs to have at least |M | vertices. Our algorithm is based on a generalization of this combinatorial lower-bound to the weighted setting.

Abstract. We present a distributed 2-approximation algorithm for the minimum vertex cover problem. The algorithm is deterministic, and it runs in ( ∆ + 1) 2 synchronous communication rounds, where ∆ is the maximum degree of the graph. For ∆ = 3, we give a 2-approximation algorithm also for the weighted version of the problem. 1

The paper presents distributed and parallel δ-approximation algorithms for covering problems, where δ is the maximum number of variables on which any constraint depends (for example, δ = 2 for vertex cover). Specific results include the following. • For weighted vertex cover, the first distributed 2-approximation algorithm taking O(log n) rounds and the first parallel 2-approximation algorithm in RNC. The algorithms generalize to covering mixed integer linear programs (CMIP) with two variables per constraint (δ = 2). • For any covering problem with monotone constraints and submodular cost, a distributed δ-approximation algorithm taking O(log² |C|) rounds, where |C| is the number of constraints. (Special cases include CMIP, facility location, and probabilistic (two-stage) variants of these problems.)

Fault tolerance is one of the main concepts in distributed computing. It has been tackled from different angles, e.g. by building replicated systems that can survive crash failures of individual components, or even systems that can tolerate a minority of arbitrarily malicious (“Byzantine”) participants.