k-Clustering partitions a set of n points in a metric space into at most k clusters in a way that makes the resulted clusters satisfy both the homogeneity and the separation criteria. The diameter of a cluster is the ...
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k-Clustering partitions a set of n points in a metric space into at most k clusters in a way that makes the resulted clusters satisfy both the homogeneity and the separation criteria. The diameter of a cluster is the maximum distance between pairs of points in the cluster, and the split of a cluster is the minimum distance between points of the cluster and ones outside the cluster. In this paper, we propose a new criterion for measuring the goodness of clusters: The ratio of the minimum cluster split to the maximum cluster diameter (abbr. RSD). We study the following two optimization problems: Maximizing RSD without and with cardinality constraints, i.e., each cluster should consist of at least N points. For both problems with k >= 3, it is NP-hard to achieve a factor of (1/2 + epsilon) approximation for any epsilon > 0. For k = 2, we solve the two problems optimally;For k >= 3, we present a 1/2-approximation and a 1/2-approximation algorithm for the two problems, respectively. (C) 2021 Elsevier B.V. All rights reserved.
One important problem that is insufficiently studied is finding densest lasting-subgraphs in large dynamic graphs, which considers the time duration of the subgraph pattern. We propose a framework called Expectation-M...
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One important problem that is insufficiently studied is finding densest lasting-subgraphs in large dynamic graphs, which considers the time duration of the subgraph pattern. We propose a framework called Expectation-Maximization with Utility functions (EMU), a novel stochastic approach that nontrivially extends the conventional EM approach. EMU has the flexibility of optimizing any user-defined utility functions. We validate our EMU approach by showing that it converges to the optimum-by proving that it is a specification of the general Minorization-Maximization (MM) framework with convergence guarantees. We devise EMU algorithms for the densest lasting subgraph problem, as well as several variants by varying the utility function. Using real-world data, we evaluate the effectiveness and efficiency of our techniques, and compare them with two prior approaches on dense subgraph detection.
In the CO-PATH PACKING (resp., CO-PATH/CYCLE PACKING) problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G results in a graph wh...
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In the CO-PATH PACKING (resp., CO-PATH/CYCLE PACKING) problem, the input is a graph G and an integer k, and the goal is to decide whether there is a set of at most k vertices whose removal from G results in a graph which is a collection of induced paths (resp., induced paths and cycles). In this paper we give deterministic O* (3(k))-time algorithms for CO-PATH PACKING and CO-PATH/CYCLE PACKING.
We give a complete structural description of ( 4 K 1 , C 4 , C 6 , C 7 )-free graphs that do not contain a simplicial vertex, and we prove that such graphs have bounded clique-width. Together with the results of Foley...
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We give a complete structural description of ( 4 K 1 , C 4 , C 6 , C 7 )-free graphs that do not contain a simplicial vertex, and we prove that such graphs have bounded clique-width. Together with the results of Foley et al., this implies that ( 4 K 1 , C 4 , C 6 )-free graphs that do not contain a simplicial vertex have bounded clique-width. Consequently, graph Coloring can be solved in polynomial time for ( 4 K 1 , C 4 , C 6 )-free graphs, that is, for even-hole-free graphs of stability number at most three.
The randomized online-LOCAL model captures a number of models of computing;it is at least as strong as all of these models: the classical LOCAL model of distributed graph algorithms, the quantum version of the LOCAL m...
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In this paper, we investigate the Grundy Coloring problem for graphs with a cluster modulator, a structure commonly found in dense graphs. The Grundy chromatic number, representing the maximum number of colors needed ...
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Frequent sub graph mining is an important and well-studied problem with numerous applications such as the prediction of protein functionalities and graph indexing. Many studies use the minimum image-based support (MNI...
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The classic greedy coloring algorithm considers the vertices of an input graph G in a given order and assigns the first available color to each vertex v in G. In the Grundy Coloring problem, the task is to find an ord...
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A connected graph has a (k,)-cover if each of its edges is contained in at least cliques of order k. Motivated by recent advances in extremal combinatorics and the literature on edge modification problems, we study th...
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graph cut algorithms are popular in optimization tasks related to min-cut and max-flow problems. However, modern FPGA graph cut algorithm accelerators still need performance and memory resource utilization optimizatio...
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