This paper introduces a new distributed data object called Resource Controller which provides an abstraction for managing the consumption of a global resource in a distributed system. Examples of resources that may be managed by such an object include; number of messages sent, number of nodes participating in the protocol, and total CPU time consumed. The Resource Controller object is accessed through a procedure that can be invoked at any node in the network. Before consuming a unit of resource at some node, the controlled algorithm should invoke the procedure at this node, requesting a permit to consume a unit of the resource. The procedure returns either a permit or a rejection. The key characteristics of the Resource Controller object are the constraints that it imposes on the global resource consumption. An (M; W)-Controller guarantees that the total number of permits granted is at most M ; it also ensures that if a request is rejected then at least M \Gamma W permits a...

Finding the connected components of an undirected graph G = (V; E) on n = jV j vertices and m = jEj edges is a fundamental computational problem. The best known parallel algorithm for the CREW PRAM model runs in O(log 2 n) time using n 2 = log 2 n processors [6, 15]. For the CRCW PRAM model, in which concurrent writing is permitted, the best known algorithm runs in O(log n) time using slightly more than (n +m)= log n processors [26, 9, 5]. Simulating this algorithm on the weaker CREW model increases its running time to O(log 2 n) [10, 19, 29]. We present here a simple algorithm that runs in O(log 3=2 n) time using n +m CREW processors. Finding an o(log 2 n) parallel connectivity algorithm for this model was an open problem for many years. 1 Introduction Let G = (V; E) be an undirected graph on n = jV j vertices and m = jEj edges. A path p of length k is a sequence of edges (e 1 ; \Delta \Delta \Delta ; e i ; \Delta \Delta \Delta ; e k ) such that e i 2 E for i = 1; \...

We introduce Multi-Trials, a new technique for symmetry breaking for distributed algorithms and apply it to various problems in general graphs. For instance, we present three randomized algorithms for distributed (vertex or edge) coloring improving on previous algorithms and showing a time/color trade-off. To get a ∆ + 1 coloring takes time O(log ∆ + √ log n). To obtain an O( ∆ + log 1+1 / log ∗ n n) coloring takes time O(log ∗ n). This is more than an exponential improvement in time for graphs of polylogarithmic degree. Our fastest algorithm works in constant time using O( ∆ log (c) n + log 1+1/c n) colors, where c denotes an arbitrary constant and log (c) n denotes the c times (recursively) applied logarithm to n. We also use the Multi-Trials technique to compute network decompositions and to compute maximal independent set (MIS), obtaining new results for several graph classes.

The first half of the paper is a general introduction which emphasizes the central role that the PRAM model of parallel computation plays in algorithmic studies for parallel computers. Some of the collective knowledge-base on non-numerical parallel algorithms can be characterized in a structural way. Each structure relates a few problems and technique to one another from the basic to the more involved. The second half of the paper provides a bird's-eye view of such structures for: (1) list, tree and graph parallel algorithms; (2) very fast deterministic parallel algorithms; and (3) very fast randomized parallel algorithms. 1 Introduction Parallelism is a concern that is missing from "traditional" algorithmic design. Unfortunately, it turns out that most efficient serial algorithms become rather inefficient parallel algorithms. The experience is that the design of parallel algorithms requires new paradigms and techniques, offering an exciting intellectual challenge. We note that it had...

The problem of finding an implicit representation for a graph such that vertex adjacency can be tested quickly is fundamental to all graph algorithms. In particular, it is possible to represent sparse graphs on n vertices using O(n) space such that vertex adjacency is tested in O(1) time. We show here how to construct such a representation efficiently by providing simple and optimal algorithms, both in a sequential and a parallel setting. Our sequential algorithm runs in O(n) time. The parallel algorithm runs in O(log n) time using O(n=log n) CRCW PRAM processors, or in O(log n log n) time using O(n = log n log

) 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...

We study the problem of the amount of information (advice) about a graph that must be given to its nodes in order to achieve fast distributed computations. The required size of the advice enables to measure the information sensitivity of a network problem. A problem is information sensitive if little advice is enough to solve the problem rapidly (i.e., much faster than in the absence of any advice), whereas it is information insensitive if it requires giving a lot of information to the nodes in order to ensure fast computation of the solution. In this paper, we study the information sensitivity of distributed graph coloring.

We study the distributed maximal independent set (henceforth, MIS) problem on sparse graphs. Currently, there are known algorithms with a sublogarithmic running time for this problem on oriented trees and graphs of bounded degrees. We devise the first sublogarithmic algorithm for computing MIS on graphs of bounded arboricity. This is a large family of graphs that includes graphs of bounded degree, planar graphs, graphs of bounded genus, graphs of bounded treewidth, graphs that exclude a fixed minor, and many other graphs. We also devise efficient algorithms for coloring graphs from these families. These results are achieved by the following technique that may be of independent interest. Our algorithm starts with computing a certain graph-theoretic structure, called Nash-Williams forests-decomposition. Then this structure is used to compute the MIS or coloring. Our results demonstrate that this methodology is very powerful. Finally, we show nearly-tight lower bounds on the running time of any distributed algorithm for computing a forestsdecomposition.

We consider a connected undirected graph G(n; m) with n nodes and m edges. A k-dominating set D in G is a set of nodes having the property that every node in G is at most k edges away from at least one node in D.

The distributed ( ∆ + 1)-coloring problem is one of most fundamental and well-studied problems in Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current state-of-the-art running time is O( ∆ log ∆+log ∗ n), due to Kuhn and Wattenhofer, PODC’06. Linial (FOCS’87) has proved a lower bound of 1 2 log ∗ n for the problem, and Szegedy and Vishwanathan (STOC’93) provided a heuristic argument that shows that algorithms from a wide family of locally iterative algorithms are unlikely to achieve running time smaller than Θ( ∆ log ∆). We present a deterministic (∆+1)-coloring distributed algorithm with running time O(∆)+ 1