With the increase in popularity of graph structured data arising in different areas such as Web, social network, communication network, knowledge graph, etc., there is a growing need for partitioning and repartitionin...
详细信息
With the increase in popularity of graph structured data arising in different areas such as Web, social network, communication network, knowledge graph, etc., there is a growing need for partitioning and repartitioning large graph data in a distributed system. However, the existing graph repartitioning methods are known for poor efficiency in the distributed environment and most of them lack a balance mechanism between edge cut and load balance. In this article, we introduce a new two-phase method to improve the result of distributed graph repartitioning. We first design a local method to identify all the potential candidate vertices that could improve the graph repartitioning result in load balance and edge cut at once in each partition locally. After that, we propose to migrate the selected vertices among the given initial partitions to improve the result of graph repartitioning. During this procedure, we propose to adopt a synchronous vertex migration method to balance both the edge cuts and load balance problems. Extensive experimental results demonstrate that the proposed method is more efficient than the existing methods in several aspects such as communication cost, running time, edge cut, and load balance. We also run SSSP and PageRank applications based on the graph repartitioning result on Giraph to indicate the efficiency of the proposed method.
A set D subset of V of a graph G = (V, E) is called a connected power dominating set of G if G[D], the subgraph induced by D, is connected and every vertex in the graph can be observed from D, following the two observ...
详细信息
A set D subset of V of a graph G = (V, E) is called a connected power dominating set of G if G[D], the subgraph induced by D, is connected and every vertex in the graph can be observed from D, following the two observation rules for power system monitoring: Rule 1: if v epsilon D, then v can observe itself and all its neighbors, and Rule 2: for an already observed vertex whose all neighbors except one are observed, then the only unobserved neighbor becomes observed as well. Given a graph G, Minimum Connected Power Domination is to find a connected power dominating set of minimum cardinality of G and Decide Connected Power Domination is the decision version of Minimum Connected Power Domination. Decide Connected Power Domination is known to be NP-complete for general graphs. In this paper, we prove that Decide Connected Power Domination remains NP-complete for star-convex bipartite graphs, perfect elimination bipartite graphs and split graphs. This answers some open problems posed in [B. Brimkov, D. Mikesell and L. Smith, Connected power domination in graphs, J. Comb. Optim. 38(1) (2019) 292{315]. On the positive side, we show that Minimum Connected Power Domination is polynomial-time solvable for chain graphs, a proper subclass of perfect elimination bipartite graph, and for threshold graphs, a proper subclass of split graphs. Further, we show that Minimum Connected Power Domination cannot be approximated within (1- epsilon) ln vertical bar V vertical bar for any epsilon > 0 unless P = NP, for bipartite graphs as well as for chordal graphs. Finally, we show that Minimum Connected Power Domination is APX-hard for bounded degree graphs.
In EMF models, ordered collections appear as the values of multi-valued structural features. Traditional, text-based version control systems do not sufficiently support three-way merging of ordered collections inside ...
详细信息
In EMF models, ordered collections appear as the values of multi-valued structural features. Traditional, text-based version control systems do not sufficiently support three-way merging of ordered collections inside EMF models since they cannot guarantee a consistent result. The operation three-way merging is defined as follows: based on a common base version b, two alternative versions a(1) and a(2) were developed by copying and modifying the base version. To reconcile these changes, a merged version m is to be created as a common successor of a(1) and a(2). In this paper, we present a graph algorithm to solve the problem of three-way merging of ordered collections in EMF models. Each version of a collection can be represented by means of a linearly ordered graph. To create the merged version, these graphs are combined to a merged collection graph using set formula. To create the merged collection, a generalized topological sort is performed on the merged collection graph. Conflicts occur in case the order of elements cannot be deduced automatically;these conflicts are resolved either interactively or by default rules. We have implemented the merge algorithm in our tool BTMerge, which performs a consistency-preserving three-way merge of versions of EMF models being instances of arbitrary Ecore models. Our implementation relies on an alternative form of representing multiple versions of a collection, namely a versioned collection graph which forms a superimposition of collection versions. The algorithm presented here is purely state-based. Matching and merging of collections are clearly separated sub-problems. Insertions and deletions performed on the elements of the collection are propagated into the merged version in a consistent way. Our algorithm makes only minimal assumptions with regard to the underlying product model and thus may be applied to ordered collections inside plain text or XML files. By taking arbitrary move operations into account, the algorithm
A signed graph offers richer information than an unsigned graph, since it describes both collaborative and competitive relationships in social networks. In this paper, we study opinion dynamics on a signed graph, base...
详细信息
A signed graph offers richer information than an unsigned graph, since it describes both collaborative and competitive relationships in social networks. In this paper, we study opinion dynamics on a signed graph, based on the Friedkin-Johnsen model. We first interpret the equilibrium opinion in terms of a defined random walk on an augmented signed graph, by representing the equilibrium opinion of every node as a combination of all nodes' internal opinions, with the coefficient of the internal opinion for each node being the difference of two absorbing probabilities. We then quantify some relevant social phenomena and express them in terms of the & ell;(2) norms of vectors. We also design a nearly-linear time signed Laplacian solver for assessing these quantities, by establishing a connection between the absorbing probability of random walks on a signed graph and that on an associated unsigned graph. We further study the opinion optimization problem by changing the initial opinions of a fixed number of nodes, which can be optimally solved in cubic time. We provide a nearly-linear time algorithm with an error guarantee to approximately solve the problem. Finally, we execute extensive experiments on sixteen real-life signed networks, which show that both of our algorithms are effective and efficient, and are scalable to massive graphs with over 20 million nodes.
graph structures have shown to represent a viable approach to developingAGI. This paper describes howa knowledge graph could be represented in neurons and introduces theUniversal Knowledge Store (UKS), an open-source ...
详细信息
graph structures have shown to represent a viable approach to developingAGI. This paper describes howa knowledge graph could be represented in neurons and introduces theUniversal Knowledge Store (UKS), an open-source implementation, which could form one component of AGI. Unlike backpropagationrelated systems which have only the most tenuous biological relationship, graph structures can be built from basic biological neuron models.
Many real-world graphs are temporal in nature, where the temporal information indicates when a particular edge is changed (e.g., edge insertion and deletion). Performing random walks on such temporal graphs is of para...
详细信息
ISBN:
(纸本)9781450394871
Many real-world graphs are temporal in nature, where the temporal information indicates when a particular edge is changed (e.g., edge insertion and deletion). Performing random walks on such temporal graphs is of paramount value. The state-of-the-art sampling strategies are tailored for conventional static graphs and thus cannot effectively tackle the dynamic nature of temporal graphs due to several significant efficiency challenges, i.e., high sampling complexity, gigantic index space, and poor programmability. In this paper, we present TEA, the first highly-efficient general-purpose TEmporal graph random walk engine. At its core, TEA introduces a new hybrid sampling approach that combines two Monte Carlo sampling methods together to drastically reduce space complexity and achieve high sampling speed. TEA further employs a series of algorithmic and system-level optimizations to remarkably improve the sampling efficiency, as well as provide streaming graph support. Finally, we introduce a temporal-centric programming model to ease the implementation of various random walk algorithms on temporal graphs. Experimental results demonstrate that TEA can achieve up to 3 orders of magnitude speedups over the state-of-the-art random walk engines on large temporal graphs.
The Gomory-Hu tree or cut tree [R. E. Gomory and T. C. Hu, J. Soc. Indust. Appl. Math., 9 (1961), pp. 55--570] is a classic data structure for reporting (s,t)-mincuts (and by duality, the values of (s, t)-maxflows) fo...
详细信息
The Gomory-Hu tree or cut tree [R. E. Gomory and T. C. Hu, J. Soc. Indust. Appl. Math., 9 (1961), pp. 55--570] is a classic data structure for reporting (s,t)-mincuts (and by duality, the values of (s, t)-maxflows) for all-pairs of vertices s and t in an undirected graph. Gomory and Hu showed that it can be computed using n - 1 exact maxflow computations. Surprisingly, this remains the best algorithm for Gomory-Hu trees more than 50 years later, even for approximate mincuts. In this paper, we break this longstanding barrier and give an algorithm for computing a (1+e)-approximate Gomory-Hu tree using polylog(n) maxflow computations. Specifically, we obtain the running time bounds we describe below. We obtain a randomized (Monte Carlo) algorithm for undirected, weighted graphs that runs in O(m + n(3/2)) time and returns a (1+e)-approximate Gomory-Hu tree with high probability (w.h.p.). Previously, the best running time known was O(n(5/2)), which is obtained by running Gomory and Hu's original algorithm on a cut sparsifier of the graph. Next, we obtain a randomized (Monte Carlo) algorithm for undirected, unweighted graphs that runs in m(4/3+o(1)) time and returns a (1 + e)-approximate Gomory-Hu tree w.h.p. This improves on our first result for sparse graphs, namely m = o(n(9/8)). Previously, the best running time known for unweighted graphs was O(mn) for an exact Gomory-Hu tree [A. Bhalgat et al., Proceedings of the 39th Annual ACM Symposium on Theory of Computing, San Diego, CA, 2007, pp. 605-614];no better result is known if approximations are allowed. As a consequence of our Gomory-Hu tree algorithms, we also solve the (1+e)-approximate all-pairs mincut (APMC) and single-source mincut (SSMC) problems in the same time bounds. (These problems are simpler in that the goal is to only return the (s, t)-mincut values, and not the mincuts.) This improves on the recent algorithm for these problems in O(n(2)) time due to Abboud, Krauthgamer, and Trabelsi [2020 IEEE 61st Annu
Clique is one of the most fundamental models for cohesive subgraph mining in network analysis. Existing clique model mainly focuses on unsigned networks. However, in real world, many applications are modeled as signed...
详细信息
Clique is one of the most fundamental models for cohesive subgraph mining in network analysis. Existing clique model mainly focuses on unsigned networks. However, in real world, many applications are modeled as signed networks with positive and negative edges. As the signed networks hold their own properties different from the unsigned networks, the existing clique model is inapplicable for the signed networks. Motivated by this, we propose the balanced clique model that considers the most fundamental and dominant theory, structural balance theory, for signed networks. Following the balanced clique model, we study the maximal balanced clique enumeration problem (MBCE) which computes all the maximal balanced cliques in a given signed network. Moreover, in some applications, users prefer a unique and representative balanced clique with maximum size rather than all balanced cliques. Thus, we also study the maximum balanced clique search problem (MBCS) which computes the balanced clique with maximum size. We show that MBCE problem and MBCS problem are both NP-Hard. For the MBCE problem, a straightforward solution is to treat the signed network as two unsigned networks and leverage the off-the-shelf techniques for unsigned networks. However, such a solution is inefficient for large signed networks. To address this problem, in this paper, we first propose a new maximal balanced clique enumeration algorithm by exploiting the unique properties of signed networks. Based on the new proposed algorithm, we devise two optimization strategies to further improve the efficiency of the enumeration. For the MBCS problem, we first propose a baseline solution. To overcome the huge search space problem of the baseline solution, we propose a new search framework based on search space partition. To further improve the efficiency of the new framework, we propose multiple optimization strategies regarding to redundant search branches and invalid candidates. We conduct extensive experiments
Given a graph G = (V, E), an L(2, 1)-labeling of the graph is an assignment l from the vertex set to the set of nonnegative integers such that for any pair of vertices (u, v), vertical bar l(u) - l(v)vertical bar >...
详细信息
Given a graph G = (V, E), an L(2, 1)-labeling of the graph is an assignment l from the vertex set to the set of nonnegative integers such that for any pair of vertices (u, v), vertical bar l(u) - l(v)vertical bar >= 2 if u and v are adjacent, and l(u) not equal l(v) if u and v are at distance 2. The L(2, 1)-labeling problem is to minimize the range of l (i.e., max(u is an element of V)(l(u))-min(u is an element of V)(l(u))+ 1). Although the problem is generally hard to approximate within any constant factor, it was known to be approximable within factor 10.67 for unit disk graphs. This paper designs a new way of partitioning the plane into squares for periodic labeling, based on which we present an 8-approximation polynomial-time algorithm for L(2, 1)-labeling of unit disk graphs. (c) 2023 Elsevier B.V. All rights reserved.
In this paper, we investigate the complexity of the MAXIMUM HAPPY SET problem on subclasses of co-comparability graphs. For a graph G and its vertex subset S, a vertex v is an element of S is happy if all v's neig...
详细信息
In this paper, we investigate the complexity of the MAXIMUM HAPPY SET problem on subclasses of co-comparability graphs. For a graph G and its vertex subset S, a vertex v is an element of S is happy if all v's neighbors in G are contained in S. Given a graph G and a non negative integer k, MAXIMUM HAPPY SET is the problem of finding a vertex subset S of G such that |S| = k and the number of happy vertices in S is maximized. In this paper, we first show that MAXIMUM HAPPY SET is NP-hard even for co-bipartite graphs. We then give an algorithm for n-vertex interval graphs whose running time is O(n(2) + k(3)n);this improves the best known running time O(kn(8)) for interval graphs. We also design algorithms for n-vertex permutation graphs and d-trapezoid graphs which run in O(n(2)+k(3)n) and O(n(2)+d(2)(k+1)(3d)n) time, respectively. These algorithmic results provide a nice contrast to the fact that MAXIMUM HAPPY SET remains NP-hard for chordal graphs, comparability graphs, and co-comparability graphs.
暂无评论