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# A Polynomial-Delay Algorithm for Enumerating Connectors Under Various Connectivity Conditions

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LIPIcs.ISAAC.2019.3.pdf
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## Cite As

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)
https://doi.org/10.4230/LIPIcs.ISAAC.2019.3

## Abstract

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.

## Subject Classification

##### ACM Subject Classification
• Mathematics of computing → Graph enumeration
##### Keywords
• Graph with itemsets
• Enumeration
• Polynomial-delay algorithms
• Connectors

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