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

We are given an instance (G, I, σ) with a graph G = (V,E), a set I of items, and a function σ : V → 2 . For a subset X of V , let G[X] denote the subgraph induced from G by X, and Iσ(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 ∈ V \X, G[X ∪ {v}] is not connected or Iσ(X ∪ {v}) is a proper subset of Iσ(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. 2012 ACM Subject Classification Mathematics of computing → Graph enumeration

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