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**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

We are given an instance (G,I,sigma) with a graph G=(V,E), a set I of items, and a function sigma:V -> 2^I. For a subset X of V, let G[X] denote the subgraph induced from G by X, and I_sigma(X) denote the common item set over X. A subset X of V such that G[X] is connected is called a connector if, for any vertex v in V\X, G[X cup {v}] is not connected or I_sigma(X cup {v}) is a proper subset of I_sigma(X).
In this paper, we present the first polynomial-delay algorithm for enumerating all connectors. For this, we first extend the problem of enumerating connectors to a general setting so that the connectivity condition on X in G can be specified in a more flexible way. We next design a new algorithm for enumerating all solutions in the general setting, which leads to a polynomial-delay algorithm for enumerating all connectors for several connectivity conditions on X in G, such as the biconnectivity of G[X] or the k-edge-connectivity among vertices in X in G.

Kazuya Haraguchi and Hiroshi Nagamochi. A Polynomial-Delay Algorithm for Enumerating Connectors Under Various Connectivity Conditions. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 3:1-3:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{haraguchi_et_al:LIPIcs.ISAAC.2019.3, author = {Haraguchi, Kazuya and Nagamochi, Hiroshi}, title = {{A Polynomial-Delay Algorithm for Enumerating Connectors Under Various Connectivity Conditions}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {3:1--3:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.3}, URN = {urn:nbn:de:0030-drops-114990}, doi = {10.4230/LIPIcs.ISAAC.2019.3}, annote = {Keywords: Graph with itemsets, Enumeration, Polynomial-delay algorithms, Connectors} }

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**Published in:** LIPIcs, Volume 103, 17th International Symposium on Experimental Algorithms (SEA 2018)

In the present paper, we propose an efficient local search for the minimum independent dominating set problem. We consider a local search that uses k-swap as the neighborhood operation. Given a feasible solution S, it is the operation of obtaining another feasible solution by dropping exactly k vertices from S and then by adding any number of vertices to it. We show that, when k=2, (resp., k=3 and a given solution is minimal with respect to 2-swap), we can find an improved solution in the neighborhood or conclude that no such solution exists in O(n Delta) (resp., O(n Delta^3)) time, where n denotes the number of vertices and Delta denotes the maximum degree. We develop a metaheuristic algorithm that repeats the proposed local search and the plateau search iteratively, where the plateau search examines solutions of the same size as the current solution that are obtainable by exchanging a solution vertex and a non-solution vertex. The algorithm is so effective that, among 80 DIMACS graphs, it updates the best-known solution size for five graphs and performs as well as existing methods for the remaining graphs.

Kazuya Haraguchi. An Efficient Local Search for the Minimum Independent Dominating Set Problem. In 17th International Symposium on Experimental Algorithms (SEA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 103, pp. 13:1-13:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{haraguchi:LIPIcs.SEA.2018.13, author = {Haraguchi, Kazuya}, title = {{An Efficient Local Search for the Minimum Independent Dominating Set Problem}}, booktitle = {17th International Symposium on Experimental Algorithms (SEA 2018)}, pages = {13:1--13:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-070-5}, ISSN = {1868-8969}, year = {2018}, volume = {103}, editor = {D'Angelo, Gianlorenzo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2018.13}, URN = {urn:nbn:de:0030-drops-89484}, doi = {10.4230/LIPIcs.SEA.2018.13}, annote = {Keywords: Minimum independent dominating set problem, local search, plateau search, metaheuristics} }