Distributed Graph Algorithm Research Articles

Distributed half-integral matching and beyond

By prior work, it is known that any distributed graph algorithm that finds a maximal matching requires Ω(log⁎⁡n) communication rounds, while it is possible to find a maximal fractional matching in O(1) rounds in bounded-degree graphs. However, all prior O(1)-round algorithms for maximal fractional matching use arbitrarily fine-grained fractional values. In particular, none of them is able to find a half-integral solution, using only values from {0,12,1}. We show that the use of fine-grained fractional values is necessary, and moreover we give a complete characterization on exactly how small values are needed: if we consider maximal fractional matching in graphs of maximum degree Δ=2d, and any distributed graph algorithm with round complexity T(Δ) that only depends on Δ and is independent of n, we show that the algorithm has to use fractional values with a denominator at least 2d. We give a new algorithm that shows that this is also sufficient.

Introduction to local certification

A distributed graph algorithm is basically an algorithm where every node of a graph can look at its neighborhood at some distance in the graph and chose its output. As distributed environment are subject to faults, an important issue is to be able to check that the output is correct, or in general that the network is in proper configuration with respect to some predicate. One would like this checking to be very local, to avoid using too much resources. Unfortunately most predicates cannot be checked this way, and that is where certification comes into play. Local certification (also known as proof-labeling schemes, locally checkable proofs or distributed verification) consists in assigning labels to the nodes, that certify that the configuration is correct. There are several point of view on this topic: it can be seen as a part of self-stabilizing algorithms, as labeling problem, or as a non-deterministic distributed decision. This paper is an introduction to the domain of local certification, giving an overview of the history, the techniques and the current research directions.

Distributed Graph Algorithms for Multiple Vector Engines of NEC SX-Aurora TSUBASA Systems

This paper describes the world-first attempt to develop distributed graph algorithm implementations, aimed for modern NEC SX-Aurora TSUBASA vector systems. Such systems are equipped with up to eight powerful vector engines, which are capable to significantly accelerate graph processsing and simultaneously increase the scale of processed input graphs. This paper describes distributed implementations of three widely-used graph algorithms: Page Rank (PR), Bellman-Ford Single Source Shortest Paths (further referred as SSSP) and Hyperlink-Induced Topic Search (HITS), evaluating their performance and scalability on Aurora 8 system. In this paper we describe graph partitioning strategies, communication strategies, programming models and single-VE optimizations used in these implementations. The developed implementations achieve 40, 6.6 and 1.3 GTEPS performance on PR, SSSP and HITS algorithm on 8 vector engines, at the same time achieving up to 1.5x, 2x and 2.5x acceleration on 2, 4 and 8 vector engines of Aurora 8 systems. Finally, this paper describes an approach to incorporate distributed graph processing support into our previously developed Vector Graph Library (VGL) framework – a novel framework for graph analytics on NEC SX-Aurora TSUBASA architecture.

A Distributed Graph Algorithm for Geometric Routing in Ad Hoc Wireless Networks

This paper presented a fully distributed algorithm to compute a planar subgraph of the underlying wireless connectivity graph. This work considered the idealized unit disk graph model in which nodes are assumed to be connected if, and only if, nodes are within their transmission range. The main contribution of this work is a fully distributed algorithm to extract the connected, planar graph for routing in the wireless networks. The communication cost of the proposed algorithm is O(d log d) bits, where d is the degree of a node. In addition, this paper also presented a geometric routing algorithm and established its lower bound. The algorithm is fully distributed and nodes know only the position of other nodes and can communicate with neighboring nodes in their transmission range.

A Message-Optimal Distributed Graph Algorithm: Partial Precedence Constrained Scheduling

A Message-Optimal Distributed Graph Algorithm: Partial Precedence Constrained Scheduling

A distributed graph algorithm for the detection of local cycles and knots

In this paper, a distributed cycle/knot detection algorithm for general graphs is presented. The algorithm distinguishes between cycles and knots and is the first algorithm to our knowledge which does so. It is especially relevant to an application such as parallel simulation in which 1) cycles and knots can arise frequently 2) the size of the graph is very large, and 3) it is necessary to know if a given node is in a cycle or a knot. It requires less communication than previous algorithms-2m vs. (at least) (4m) for the Chandy and Misra algorithm, where m is the number of links in the graph. It requires O (nlog (n)) bits of memory, where n is the number of nodes. The algorithm differs from the classical diffusing computation methods through its use of incomplete search messages to speed up the computation. We introduce a marking scheme in order to identify strongly connected subcomponents of the graph which cannot reach the initiator of the algorithm. This allows us to distinguish between the case in which the initiator is in a cycle (only) or is in a knot.

A Distributed Graph Algorithm: Knot Detection

Abstract : A knot in a directed graph is a useful concept in deadlock detection. This paper presents a distributed algorithm based on the work of Dijkstra and Scholten to identify knot in a graph by using a network of processes. (Author)