We propose a new data structure for representing all distances in a graph that is based on 2-hop covers of the shortest paths, or of all paths, in the graph.Expand

We prove that if the d-regular multigraph does not contain more than ⌊d/2⌋ copies of any 2-cycles then we can find a similar decomposition into n2 pairs of cycle covers where each 2-cycle occurs in at most one component of each pair.Expand

We consider the following problem. Give a rooted tree T, label the nodes of T in the most compact way such that given the labels of two nodes one can determine in constant time, by looking only at… Expand

A new algorithm that labels the nodes of a rooted tree such that from the labels of two nodes alone one can compute in constant time the label of their nearest common ancestor.Expand

We show that four simplified models of the problem lead to NP-complete decision problems: Colored unit interval graph completion, the maximum interval (or unit interval) subgraph, the pathwidth of a bipartite graph, and the k-consecutive ones problem.Expand

We study the parameterized complexity of three NP-hard graph completion problems.
The minimum fill-in problem asks if a graph can be triangulated by adding at most k edges. We develop O(ck m) and… Expand