We are given an instance (G,I,s) with a graph G=(V,E),
a set I of items, and a function s from V to I.
For a subset X of V,
let G[X] denote the subgraph induced from G by X,
and Item(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 $vin Vsetminus X$,
G[X cup {v}] is not connected or Item(X cup {v})
is a proper subset of Item(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.