Learn More
Traffic grooming is a central problem in optical networks. It refers to pack low rate signals into higher speed streams, in order to improve bandwidth utilization and reduce network cost. In WDM networks, the most accepted criterion is to minimize the number of electronic terminations, namely the number of SONET Add-Drop Multiplexers (ADMs). In this article(More)
We present a linear-time algorithm to compute a decomposition scheme for graphs <i>G</i> that have a set <i>X</i>&#8838;<i>V</i>(<i>G</i>), called a <i>treewidth-modulator</i>, such that the treewidth of <i>G</i> &minus; <i>X</i> is bounded by a constant. Our decomposition, called a <i>protrusion decomposition</i>, is the cornerstone in obtaining the(More)
We provide a framework for the design and analysis of dynamic programming algorithms for surface-embedded graphs on <i>n</i> vertices and branchwidth at most <i>k</i>. Our technique applies to general families of problems where standard dynamic programming runs in 2<sup><i>O</i>(<i>k</i>&#7777;log <i>k</i>)</sup> &#7777; <i>n</i> steps. Our approach(More)
A general instance of a Degree-Constrained Subgraph problem consists of an edge-weighted or vertex-weighted graph G and the objective is to find an optimal weighted subgraph, subject to certain degree constraints on the vertices of the subgraph. This paper considers two natural Degree-Constrained Subgraph problems and studies their behavior in terms of(More)
The c-pumpkin is the graph with two vertices linked by c ≥ 1 parallel edges. A c-pumpkin-model in a graph G is a pair {A,B} of disjoint subsets of vertices of G, each inducing a connected subgraph of G, such that there are at least c edges in G between A and B. We focus on covering and packing c-pumpkin-models in a given graph: On the one hand, we provide(More)
The theory of Graph Minors by Robertson and Seymour is one of the deepest and significant theories in modern Combinatorics. This theory has also a strong impact on the recent development of Algorithms, and several areas, like Parameterized Complexity, have roots in Graph Minors. Until very recently it was a common belief that Graph Minors Theory is mainly(More)
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This class of graphs, which generalizes in a natural way both interval and permutation graphs, has attracted many research efforts since their introduction in [M. C. Golumbic and C. L. Monma, Congr. Numer., 35 (1982),(More)
The placement of regenerators in optical networks has become an active area of research during the last few years. Given a set of lightpaths in a network <i>G</i> and a positive integer <i>d</i>, regenerators must be placed in such a way that in any lightpath there are no more than <i>d</i> hops without meeting a regenerator. The cost function we consider(More)
For every r ∈ N, we denote by θr the multigraph with two vertices and r parallel edges. Given a graph G, we say that a subgraph H of G is a model of θr in G if H contains θr as a contraction. We prove that the following edge variant of the Erdős–Pósa property holds for every r > 2: if G is a graph and k is a positive integer, then either G contains a(More)
In this article we study the parameterized complexity of problems consisting in finding degree-constrained subgraphs, taking as the parameter the number of vertices of the desired subgraph. Namely, given two positive integers d and k, we study the problem of finding a d-regular (induced or not) subgraph with at most k vertices and the problem of finding a(More)