The Labeled Two Edge Connected Subgraph Problem

In this paper, we address a variant of the Two Edge Connected Problem (TECP), that is the TECP with color constraint on the edges, also known as the Labeled Two Edge Connected Problem (LTECP). Given a connected undirected graph
$G$
whose edges are labeled (or colored), the LTECP consists in finding a two-edge connected spanning subgraph of
$G$
with a minimum number of distinct labels (or colors). We distinguish two variants of the problem: the first one is when each edge is associated with exactly one label (i.e., the LTECP), and the second is when each edge may be associated with more than one label. This variant is called the Generalized Labeled Two Edge Connected Problem (i.e., the GLTECP). Both problems are relevant in some application fields such as telecommunication networks or transportation networks. We propose Integer Linear Programming formulations for the two variants, we identify a new class of valid inequalities, and present preliminary computational results.