Distributed algorithm

About: Distributed algorithm is a research topic. Over the lifetime, 20416 publications have been published within this topic receiving 548109 citations.

On Hierarchical Power Scheduling for the Macrogrid and Cooperative Microgrids

Abstract: Although considerable advances have been made in single microgrid (MG) systems, the problem of cooperation among MGs and the macrogrid has attracted considerable interest only recently. As in wireless communications systems, exploiting the temporal, spatial, and technological diversities in multiple cooperative MGs could bring about more efficient power generation and distribution. This paper investigates a hierarchical power scheduling approach to optimally manage power trading, storage, and distribution in a smart power grid with a macrogrid and cooperative MGs. We first formulate the problem as a convex optimization problem and then decompose it into a two-tier formulation. The first-tier problem jointly considers user utility, transmission cost, and grid load variance, while the second-tier problem minimizes the power generation and transmission cost, and exploits distributed storage in the MGs. We develop an effective online algorithm to solve the first-tier problem and prove its asymptotic optimality, as well as a distributed optimal algorithm for solving the second-tier problem. The proposed algorithms are evaluated with trace-driven simulations and are shown to outperform several existing schemes with considerable gains.

Polylogarithmic-time deterministic network decomposition and distributed derandomization

Abstract: We present a simple polylogarithmic-time deterministic distributed algorithm for network decomposition. This improves on a celebrated 2 O(√logn)-time algorithm of Panconesi and Srinivasan [STOC’92] and settles a central and long-standing question in distributed graph algorithms. It also leads to the first polylogarithmic-time deterministic distributed algorithms for numerous other problems, hence resolving several well-known and decades-old open problems, including Linial’s question about the deterministic complexity of maximal independent set [FOCS’87; SICOMP’92]—which had been called the most outstanding problem in the area. The main implication is a more general distributed derandomization theorem: Put together with the results of Ghaffari, Kuhn, and Maus [STOC’17] and Ghaffari, Harris, and Kuhn [FOCS’18], our network decomposition implies that P-RLOCAL = P-LOCAL. That is, for any problem whose solution can be checked deterministically in polylogarithmic-time, any polylogarithmic-time randomized algorithm can be derandomized to a polylogarithmic-time deterministic algorithm. Informally, for the standard first-order interpretation of efficiency as polylogarithmic-time, distributed algorithms do not need randomness for efficiency. By known connections, our result leads also to substantially faster randomized distributed algorithms for a number of well-studied problems including (Δ+1)-coloring, maximal independent set, and Lovasz Local Lemma, as well as massively parallel algorithms for (Δ+1)-coloring.

Tight lower and upper bounds for some distributed algorithms for a complete network of processors

Abstract: Distributed algorithms for complete asynchronous networks of processors (i.e., networks where each pair of processors is connected by a communication line) are discussed. The main result is O(nlogn) lower and upper bounds on the number of messages required by any algorithm in a given class of distributed algorithms for such networks. This class includes algorithms for problems like finding a leader or constructing a spanning tree (as far as we know, all known algorithms for those problems may require O(n2) messages when applied to complete networks). O(n2) bounds for other problems, like constructing a maximal matching or a Hamiltonian circuit are also given. In proving the lower bound we are counting the edges which carry messages during the executions of the algorithms (ignoring the actually number of messages carried by each edge). Interestingly, this number is shown to be of the same order of magnitude of the total number of messages needed by these algorithms. In the upper bounds, the length of any message is at most log2[4mlog2n] bits, where m is the maximum identity of a node in the network. One implication of our results is that finding a spanning tree in a complete network is easier than finding a minimum weight spanning tree in such a network, which may require O(n2) messages.