Discovery of frequent subgraphs of a network is a challenging and time-consuming process. Several heuristics and improvements have been proposed before. However, when the size of subgraphs or the size of network is bi...
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Discovery of frequent subgraphs of a network is a challenging and time-consuming process. Several heuristics and improvements have been proposed before. However, when the size of subgraphs or the size of network is big, the process cannot be done in feasible time on a single machine. One of the promising solutions is using the processing power of available parallel and distributed systems. In this paper, we present a distributed solution for discovery of frequent subgraphs of a network using the MapReduce framework. The solution is named MRSUB and is developed to run over the Hadoop framework. MRSUB uses a novel and load-balanced parallel subgraph enumeration algorithm and fits it into the MapReduce framework. Also, a fast subgraph isomorphism detection heuristic is used which accelerates the whole process further. We executed MRSUB on a private cloud infrastructure with 40 machines and performed several experiments with different networks. Experimental results show that MRSUB scales well and offers an effective solution for discovery of frequent subgraphs of networks which are not possible on a single machine in feasible time.
Community detection has become an extremely active area of research in recent years, with researchers proposing various new metrics and algorithms to address the problem. Recently, the Weighted Community Clustering (W...
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ISBN:
(纸本)9781450334730
Community detection has become an extremely active area of research in recent years, with researchers proposing various new metrics and algorithms to address the problem. Recently, the Weighted Community Clustering (WCC) metric was proposed as a novel way to judge the quality of a community partitioning based on the distribution of triangles in the graph, and was demonstrated to yield superior results over other commonly used metrics like modularity. The same authors later presented a parallel algorithm for optimizing WCC on large graphs. In this paper, we propose a new distributed, vertex-centric algorithm for community detection using the WCC metric. Results are presented that demonstrate the algorithm's performance and scalability on up to 32 worker machines and real graphs of up to 1.8 billion edges. The algorithm scales best with the largest graphs, finishing in just over an hour for the largest graph, and to our knowledge, it is the first distributed algorithm for optimizing the WCC metric.
Konig's theorem states that on bipartite graphs the size of a maximum matching equals the size of a minimum vertex cover. It is known from prior work that for every epsilon > 0 there exists a constant-time dist...
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Konig's theorem states that on bipartite graphs the size of a maximum matching equals the size of a minimum vertex cover. It is known from prior work that for every epsilon > 0 there exists a constant-time distributed algorithm that finds a (1 + epsilon)-approximation of a maximum matching on bounded-degree graphs. In this work, we show-somewhat surprisingly-that no sublogarithmic-time approximation scheme exists for the dual problem: there is a constant delta > 0 so that no randomised distributed algorithm with running time o(log n) can find a (1 + delta)-approximation of a minimum vertex cover on 2-coloured graphs of maximum degree 3. In fact, a simple application of the Linial-Saks (Combinatorica 13:441-454, 1993) decomposition demonstrates that this run-time lower bound is tight. Our lower-bound construction is simple and, to some extent, independent of previous techniques. Along the way we prove that a certain cut minimisation problem, which might be of independent interest, is hard to approximate locally on expander graphs.
We perform an extensive experimental evaluation of very simple, distributed, randomized algorithms for(Delta+1) and so-called Brooks-Vizing vertex colorings, i.e., colorings using considerably fewer than Delta Colors ...
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We perform an extensive experimental evaluation of very simple, distributed, randomized algorithms for(Delta+1) and so-called Brooks-Vizing vertex colorings, i.e., colorings using considerably fewer than Delta Colors (here Delta denotes the maximum degree of the graph). We consider variants of algorithms known from the literature, boosting them with a distributed independent set computation. Our study clearly determines the relative performance of the algorithms with respect to the number of communication rounds and the number of colors. The results are confirmed by all the experiments and instance families. The empirical evidence shows that some algorithms use very few rounds and are rather effective, thus being amenable to be used in practice.
This paper describes a distributed algorithm for computing the biconnected components of a dynamically changing graph. Our algorithm has a worst-case communication complexity of O (b + c) messages for an edge insertio...
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This paper describes a distributed algorithm for computing the biconnected components of a dynamically changing graph. Our algorithm has a worst-case communication complexity of O (b + c) messages for an edge insertion and O (b' + c) messages for an edge removal, and a worst-case time complexity of O (c) for both operations, where c is the maximum number of biconnected components in any of the connected components during the operation, b is the number of nodes in the biconnected component containing the new edge, and b' is the number of nodes in the biconnected component just before the deletion. The algorithm is presented in two stages. First, a serial algorithm is presented in which topology updates occur one at a time. Then, building on the serial algorithm, an algorithm is presented in which concurrent update requests are serialized within each connected component. The problem is motivated by the need to implement causal ordering of messages efficiently in a dynamically changing communication structure.
Given a biconnected graph G with n vertices, m edges and a vertex r, the centering of a spanning tree problem asks for a spanning tree T of G with the given vertex r as center of T. In this paper we present an O(m) me...
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Given a biconnected graph G with n vertices, m edges and a vertex r, the centering of a spanning tree problem asks for a spanning tree T of G with the given vertex r as center of T. In this paper we present an O(m) message complexity and O(n) time complexity distributed algorithm for centering a spanning tree of a biconnected graph.
Fundamental differences are shown to exist in graph traversal techniques between serial and distributed computations in their behaviors, computational complexities, and effects on the design of graphalgorithms. Two ...
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Fundamental differences are shown to exist in graph traversal techniques between serial and distributed computations in their behaviors, computational complexities, and effects on the design of graphalgorithms. Two distributedalgorithms are presented together with their computational complexity for graph traversal based on the depth-first search and breadth-first search techniques. Several distributed versions are given of the Ford and Fulkerson algorithm for the depth-first, largest augmentation, and breadth-first search methods. A worst case upper bound on the number of messages transmitted also is acquired for each of these versions. As in the case of serial computation, these complexity results do not clearly indicate that one of these methods is superior to the others. However, combining these bounds with empirical results indicates that, in distributed computation, largest augmentation appears to be a better method than the other 2.
We develop a general deterministic distributed method for locally rounding fractional solutions of graph problems for which the analysis can be broken down into analyzing pairs of vertices. Roughly speaking, the metho...
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We develop a general deterministic distributed method for locally rounding fractional solutions of graph problems for which the analysis can be broken down into analyzing pairs of vertices. Roughly speaking, the method can transform fractional/probabilistic label assignments of the vertices into integral/deterministic label assignments for the vertices, while approximately preserving a potential function that is a linear combination of functions, each of which depends on at most two vertices (subject to some conditions usually satisfied in pairwise analyses). The method unifies and significantly generalizes prior work on deterministic local rounding techniques [Ghaffari, Kuhn FOCS’21; Harris FOCS’19; Fischer, Ghaffari, Kuhn FOCS’17; Fischer DISC’17] to obtain polylogarithmic-time deterministic distributed solutions for combinatorial graph problems. Our general rounding result enables us to locally and efficiently derandomize a range of distributedalgorithms for local graph problems, including maximal independent set (MIS), maximum-weight independent set approximation, and minimum-cost set cover approximation. As highlights, we in particular obtain the following results.—We obtain a deterministic \(O(\log^distributed\Delta\cdot\log n)\)-round algorithm for computing an MIS in the \(\mathsf{LOCAL}\) model and an almost as efficient \(O(\log^distributed\Delta\cdot\log\log\Delta\cdot\log n)\)-round deterministic MIS algorithm in the \(\mathsf{CONGEST}\) model. As a result, the best known deterministic distributed time complexity of the four most widely studied distributed symmetry breaking problems (MIS, maximal matching, \((\Delta+1)\)-vertex coloring, and \((2\Delta-1)\)-edge coloring) is now \(O(\log^distributed\Delta\cdot\log n)\). Our new MIS algorithm is also the first direct polylogarithmic-time deterministic distributed MIS algorithm, which is not based on network decomposition.—We obtain efficient deterministic distributedalgorithms for rounding fractional solutions for maximum (wei
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