Some Simple Distributed Algorithms for Sparse Networks

We give simple, deterministic, distributed algorithms for computing maximal matchings, maximal independent sets and colourings. We show that edge colourings with at most 2D-1 colours, and maximal matchings can be computed within O(log^* n + D) deterministic rounds, where D is the maximum degree of the network. We also show how to find maximal independent sets and (D+1)-vertex colourings within O(log^* n + D^2) deterministic rounds. All hidden constants are very small and the algorithms are very simple

Distributed Deterministic Edge Coloring using Bounded Neighborhood Independence

We study the {edge-coloring} problem in the message-passing model of distributed computing. This is one of the most fundamental and well-studied problems in this area. Currently, the best-known deterministic algorithms for (2Delta -1)-edge-coloring requires O(Delta) + log-star n time \cite{PR01}, where Delta is the maximum degree of the input graph. Also, recent results of \cite{BE10} for vertex-coloring imply that one can get an O(Delta)-edge-coloring in O(Delta^{epsilon} \cdot \log n) time, and an O(Delta^{1 + epsilon})-edge-coloring in O(log Delta log n) time, for an arbitrarily small constant epsilon > 0. In this paper we devise a drastically faster deterministic edge-coloring algorithm. Specifically, our algorithm computes an O(Delta)-edge-coloring in O(Delta^{epsilon}) + log-star n time, and an O(Delta^{1 + epsilon})-edge-coloring in O(log Delta) + log-star n time. This result improves the previous state-of-the-art {exponentially} in a wide range of Delta, specifically, for 2^{Omega(\log-star n)} \leq Delta \leq polylog(n). In addition, for small values of Delta our deterministic algorithm outperforms all the existing {randomized} algorithms for this problem. On our way to these results we study the {vertex-coloring} problem on the family of graphs with bounded {neighborhood independence}. This is a large family, which strictly includes line graphs of r-hypergraphs for any r = O(1), and graphs of bounded growth. We devise a very fast deterministic algorithm for vertex-coloring graphs with bounded neighborhood independence. This algorithm directly gives rise to our edge-coloring algorithms, which apply to {general} graphs. Our main technical contribution is a subroutine that computes an O(Delta/p)-defective p-vertex coloring of graphs with bounded neighborhood independence in O(p^2) + \log-star n time, for a parameter p, 1 \leq p \leq Delta

Parallel I/O scheduling in the presence of data duplication on multiprogrammed cluster computing systems

The widespread adoption of cluster computing as a high performance computing platform has seen the growth of data intensive scientific, engineering and commercial applications such as digital libraries, climate modeling, computational chemistry, computational fluid dynamics and image repositories. However, I/O subsystem performance has not been keeping pace with processor and memory performance, and is fast becoming the dominant factor in overall system performance.&nbsp; Thus, parallel I/O has become a necessity in the face of performance improvements in other areas of computing systems. This paper addresses the problem of parallel I/O scheduling on cluster computing systems in the presence of data replication.&nbsp; We propose two new I/O scheduling algorithms and evaluate the relative performance of the proposed policies against two existing approaches.&nbsp; Simulation results show that the proposed policies perform substantially better than the baseline policies.<br /

Efficient Parallel I/O Scheduling in the Presence of Data Duplication

This paper investigates the problem of scheduling parallel I/O operations on systems that provide data replication. The objective is to direct each compute node to access data from an I/O node where the data is duplicated, in such a way that requests for data are evenly distributed among I/O nodes. We identify a necessary and sufficient condition on whether the current data request pattern can be improved, in terms of the maximum number of data requests on any I/O node. We propose an augmenting path algorithm that examines this necessary and sufficient condition, and adjusts the current data request pattern accordingly. Using network flow technique, we show that the augmenting path algorithm finds an optimal assignment in O(nm log n+n&amp;sup2;log^(3/2) n) time

Routing and Scheduling I/O Transfers on Wormhole-Routed Mesh Networks

This paper addresses the problem of routing and scheduling parallel I/O operations to minimize the time required to transfer data between processors and I/O devices. In particular, 2-dimensional Mesh is considered in which routing is performed using wormhole switching, and I/O nodes are placed on the periphery of the mesh. Within this context, two kinds of scheduling mechanisms are studied. In the first, packets may be blocked temporarily in the network: an algorithm is presented that allocates routes based on minimizing traffic congestion on the interconnection network. In the second, a scheduling algorithm which ensures that no packet will blocked along its route is presented. This paper discusses the complexity of these problems, proposes and evaluates several heuristic algorithms, and experimentally compares the performance of blocking and non-blocking routing techniques. 1 Introduction The time required for I/O operations is known to often severely limit the performance of a par..