A Naive Algorithm for Feedback Vertex Set

Given a graph on n vertices and an integer k, the feedback vertex set problem asks for the deletion of at most k vertices to make the graph acyclic. We show that a greedy branching algorithm, which always branches on an undecided vertex with the largest degree, runs in single-exponential time, i.e., O(c^k n^2) for some constant c

Enumerating Maximal Induced Subgraphs

Given a graph G, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of G that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in literature, has been intensively studied, enumeration algorithms were only known for a few simple graph classes, e.g., independent sets, cliques, and forests, until very recently [Conte and Uno, STOC 2019]. There is also a connected variation of this problem, where one is concerned with only those induced subgraphs that are connected. We introduce two new approaches, which enable us to develop algorithms that solve both variations for a number of important graph classes. A general technique that has been proven very powerful in enumeration algorithms is to build a solution map, i.e., a multiple digraph on all the solutions of the problem, and the key of this approach is to make the solution map strongly connected, so that a simple traversal of the solution map solves the problem. First, we introduce retaliation-free paths to certify strong connectedness of the solution map we build. Second, generalizing the idea of Cohen, Kimelfeld, and Sagiv [JCSS 2008], we introduce an apparently very restricted version of the maximal (connected) induced subgraphs problem, and show that it is equivalent to the original problem in terms of solvability in incremental polynomial time. Moreover, we give reductions between the two variations, so that it suffices to solve one of the variations for each class we study. Our work also leads to direct and simpler proofs of several important known results

Neural Collective Entity Linking

Entity Linking aims to link entity mentions in texts to knowledge bases, and neural models have achieved recent success in this task. However, most existing methods rely on local contexts to resolve entities independently, which may usually fail due to the data sparsity of local information. To address this issue, we propose a novel neural model for collective entity linking, named as NCEL. NCEL applies Graph Convolutional Network to integrate both local contextual features and global coherence information for entity linking. To improve the computation efficiency, we approximately perform graph convolution on a subgraph of adjacent entity mentions instead of those in the entire text. We further introduce an attention scheme to improve the robustness of NCEL to data noise and train the model on Wikipedia hyperlinks to avoid overfitting and domain bias. In experiments, we evaluate NCEL on five publicly available datasets to verify the linking performance as well as generalization ability. We also conduct an extensive analysis of time complexity, the impact of key modules, and qualitative results, which demonstrate the effectiveness and efficiency of our proposed method.Comment: 12 pages, 3 figures, COLING201

On Fork-free T-perfect Graphs

In an attempt to understanding the complexity of the independent set problem, Chv{\'a}tal defined t-perfect graphs. While a full characterization of this class is still at large, progress has been achieved for claw-free graphs [Bruhn and Stein, Math.\ Program.\ 2012] and $P_{5}$-free graphs [Bruhn and Fuchs, SIAM J.\ Discrete Math.\ 2017]. We take one more step to characterize fork-free t-perfect graphs, and show that they are strongly t-perfect and three-colorable. We also present polynomial-time algorithms for recognizing and coloring these graphs

Bridges in three-dimensional granular packings: experiments and simulations

In this letter, we present the first experimental study of bridge structures in three-dimensional dry granular packings. When bridges are small, they are predominantly 'linear', and have an exponential size distribution. Larger, predominantly 'complex' bridges, are confirmed to follow a power-law size distribution. Our experiments, which use X-ray tomography, are in good agreement with the simulations presented here, for the distribution of sizes, end-to-end lengths, base extensions and orientations of predominantly linear bridges. Quantitative differences between the present experiment and earlier simulations suggest that packing fraction is an important determinant of bridge structure.Comment: 6 pages, 7 figures, accepted by EPL (2013