We report on a recent breakthrough in rule-based graph programming, which allows us to reach the time complexity of imperative linear-time algorithms. In general, achieving the complexity of graph algorithms in conven...
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A pangenome graph can represent the genomes of multiple individuals simultaneously. It provides a more comprehensive reference and overcomes the allele bias caused by linear reference genome, which is becoming a power...
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Stochastic optimization algorithms are widely used for large-scale data analysis due to their low per-iteration costs, but they often suffer from slow asymptotic convergence caused by inherent variance. Variance-reduc...
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Triangle counting is a critical problem in graph theory and network analysis, with widespread applications in social network analysis, network science, and bioinformatics. Dynamic graphs are extensively utilized in va...
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The application of multi-sensor (millimeter wave radar, LiDAR, binocular camera, etc.) fusion perception technology to the monitoring of cross sections of transmission lines is proposed in response to the difficulty o...
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Recent work has initiated the study of dense graph processing using graph sketching methods, which drastically reduce space costs by lossily compressing information about the input graph. In this paper, we explore the...
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We consider the problem of adding a minimum length set of edges to a geometric graph so that the resultant graph is resilient against partition from the effect of a single disaster. Disasters are modeled by discs of g...
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We consider the problem of adding a minimum length set of edges to a geometric graph so that the resultant graph is resilient against partition from the effect of a single disaster. Disasters are modeled by discs of given maximum radius, and a disaster destroys all edges intersecting its interior. It is assumed that the input and output graphs are planar with a straight-line embedding. We provide a computationally simple characterisation of feasible input instances in terms of the convex hull of the given graph, and present a fast ILP algorithm for generating optimal solutions. We also perform a computational study which shows that our algorithm is able to solve randomly generated instances with hundreds of nodes.
Finding edge-disjoint path pairs has been recognized as a vital issue in terms of the fault tolerance and survivability of networks. In many practical scenarios, in order to reduce standby and restart energy consumpti...
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Finding edge-disjoint path pairs has been recognized as a vital issue in terms of the fault tolerance and survivability of networks. In many practical scenarios, in order to reduce standby and restart energy consumption and improve data transmission efficiency, we need to consider a constraint to control the delay difference of data transmission on each common node of two edge-disjoint paths. Meanwhile, a large number of common nodes tend to cause data congestion and increase the probability that faulty common nodes break two edge-disjoint paths. Based on these, we propose the problem of finding min-min edge-disjoint path pairs under the constraints of delay difference and the number of common nodes. To address the problem, we discretize each node according to its all processing time intervals to construct an equivalent problem in an auxiliary time digraph with delay division node sets. Then, we design conflicting node exclusion (CoNE) algorithm, a heuristic algorithm, using divide-and-conquer strategy on the conflicting node set. Finally, through extensive simulations, comparing with other related algorithms, we show that CoNE is significantly effective in large-scale networks.
A cluster graph is a disjoint union of cliques, obtained by clustering the nodes of a given network and then removing the edges between nodes assigned to different clusters. The Cluster Deletion problem asks for the s...
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A cluster graph is a disjoint union of cliques, obtained by clustering the nodes of a given network and then removing the edges between nodes assigned to different clusters. The Cluster Deletion problem asks for the smallest subset of edges to be removed from a network in order to produce a cluster graph, which is equivalent to determining the largest subset of edges to be preserved. The problem finds application in many fields, including computational biology, bioinformatics, and wireless sensor networks, and it is known to be NP$$ \mathrm{NP} $$-hard on general graphs. In this work, we formulate the problem as an integer linear program, and we devise a heuristic approach based on edge contraction operations. We test the proposed approaches on both artificial instances and benchmark biological networks.
Massively-parallel graph algorithms have received extensive attention over the past decade, with research focusing on three memory regimes: the superlinear regime, the near-linear regime, and the sublinear regime. The...
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Massively-parallel graph algorithms have received extensive attention over the past decade, with research focusing on three memory regimes: the superlinear regime, the near-linear regime, and the sublinear regime. The sublinear regime is the most desirable in practice, but conditional hardness results point towards its limitations. In this work we study a heterogeneous model, where the memory of the machines varies in size. We focus mostly on the heterogeneous setting created by adding a single near-linear machine to the sublinear MPC regime, and show that even a single large machine suffices to circumvent most of the conditional hardness results for the sublinear regime: for graphs with n vertices and m edges, we give (a) an MST algorithm that runs in O(loglog(m/n)) rounds;(b) an algorithm that constructs an O(k)-spanner of size O(n(1+1/k)) in O(1) rounds;and (c) a maximal-matching algorithm that runs in O(root log(m/n)log log(m/n)) rounds. We also observe that the best known near-linear MPC algorithms for several other graph problems which are conjectured to be hard in the sublinear regime (minimum cut, maximal independent set, and vertex coloring) can easily be transformed to work in the heterogeneous MPC model with a single near-linear machine, while retaining their original round complexity in the near-linear regime. If the large machine is allowed to have superlinear memory, all of the problems above can be solved in O(1) rounds.
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