Abstract. In this paper, we study distributed algorithms to compute a weighted matching that have constant (or at least sub-logarithmic) running time and that achieve approximation ratio 2 + ɛ or better. In fact we present two such synchronous algorithms, that work on arbitrary weighted trees. The first algorithm is a randomised distributed algorithm that computes a weighted matching of an arbitrary weighted tree, that approximates the maximum weighted matching by a factor 2 + ɛ. The running time is O(1). The second algorithm is deterministic, and approximates the maximum weighted matching by a factor 2 + ɛ, but has running time O(log ∗ |V |). Our algorithms can also be used to compute maximum unweighted matchings on regular and almost regular graphs within a constant approximation. 1

Abstract — We introduce a low-complexity distributed slotted MAC protocol that can support all feasible arrival rates in a wireless backhaul network (WBN). For arbitrary wireless networks, such a maximum throughput protocol has been notoriously hard to realize because (i) even if global topology information is available, the problem of computing the optimal link transmission set at each slot is NP-complete (ii) no bounds exist on the number of steps required for such a computation (per-slot overhead). For the logical tree structures induced by the WBN traffic matrices, we first introduce a centralized algorithm that solves the optimal scheduling problem in a number of steps at most linear in the number of nodes in the network. This is achieved by discovering and exploiting a novel set of graph-theoretical properties of the WBN contention graph. Guided by the centralized algorithm, we design a distributed protocol where, at the beginning of each slot, nodes coordinate and incrementally compute the optimal link transmission set. We then introduce an algorithm to compute the minimum number of steps to complete this computation, thus minimizing the per-slot overhead. Using both analysis and simulations, we show that in practice our protocol yields low overhead when implemented over existing wireless technologies and significantly outperforms existing suboptimal distributed slotted scheduling mechanisms. I.

Abstract. We consider the problem of computing a weighted edge matching in a large graph using a parallel algorithm. This problem has application in several areas of combinatorial scientific computing. Since an exact algorithm for the weighted matching problem is both fairly expensive to compute and hard to parallelise we instead consider fast approximation algorithms. We analyse a distributed algorithm due to Hoepman [8] and show how this can be turned into a parallel algorithm. Through experiments using both complete as well as sparse graphs we show that our new parallel algorithm scales well using up to 32 processors. 1

This paper aims at achieving optimal rate allocation for data aggregation in wireless sensor networks. We first formulate this rate allocation problem as a network utility maximization problem. Due to its non-convexity, we take a couple of variable substitutions on the original problem and transform it into an approximate problem, which is convex. We then apply duality theory to decompose this approximate problem into a rate control subproblem and a scheduling subproblem. Based on this decomposition, a distributed algorithm for joint rate control and scheduling is designed, and proved to approach arbitrarily close to the optimum of the approximate problem. Finally, we show that our approximate solution can achieve near-optimal performance through both theoretical analysis and simulations.

Efficient parallel algorithms for problems such as maximum weighted matching are central to many areas of combinatorial scientific computing. Manne and Bisseling [13] presented a parallel approximation algorithm which is well suited to distributed memory computers. This algorithm is based on a distributed protocol due to Hoepman [9]. In the current paper, a partitioned global address space (PGAS) implementation is presented. PGAS programmers have the conveniences of using a shared memory model, which provides implicit communication between processes using normal loads and stores. Since the shared memory is partitioned according to the affinity of a process, one is also able to exploit data locality. This paper addresses the main differences between the PGAS and MPI implementations of the Manne-Bisseling algorithm. It highlights some advantages of using the PGAS model such as shorter, simpler code, similarity to the sequential algorithm, and options for fine-grained and coarsegrained communication. 1.