Multi-switch: A tool for finding potential edge-disjoint 1-factors

Finding Two Edge-Disjoint Paths with Length Constraints

We consider the problem of finding, for two pairs (s1, t1) and (s2, t2) of vertices in an undirected graphs, an (s1, t1)-path P1 and an (s2, t2)-path P2 such that P1 and P2 share no edges and the length of each Pi satisfies Li, where Li ∈ {≤ ki, = ki, ≥ ki, ≤ ∞}. We regard k1 and k2 as parameters and investigate the parameterized complexity of the above problem when at least one of P1 and P2 ha...

The Problem of Finding Two Edge-Disjoint Hamiltonian Cycles

Finding Disjoint Paths on Edge-Colored Graphs: More Tractability Results

The problem of finding the maximum number of vertex-disjoint uni-color paths in an edge-colored graph (MaxCDP) has been recently introduced in literature, motivated by applications in social network analysis. In this paper we investigate how the complexity of the problem depends on graph parameters (distance from disjoint paths and size of vertex cover), and that is not FPT-approximable. Moreov...

A Linear Time Algorithm for Finding Three Edge-Disjoint Paths in Eulerian Networks

Consider an undirected graph G = (V G,EG) and a set of six terminals T = {s1, s2, s3, t1, t2, t3} ⊆ V G. The goal is to find a collection P of three edge-disjoint paths P1, P2, and P3, where Pi connects nodes si and ti (i = 1, 2, 3). Results obtained by Robertson and Seymour by graph minor techniques imply a polynomial time solvability of this problem. The time bound of their algorithm is O(m) ...

Multi-scale edge finding in noisy pictures

Finding edges in digital images is a very basic and important task. This paper describes a new technique to address this problem. The proposed technique tries to solve two of the main difficulties that edge finding algorithms must face: uncertainty due to noise artifacts and combination of details detected at different scales. In particular we adapt a fuzzy arithmetic approach called “Fuzzy Mar...