In the Imbalance Minimization problem we are given a graph G = (V,E) and an integer b and asked whether there is an ordering v1 . . . vn of V such that the sum of the imbalance of all the vertices is at most b. The imbalance of a vertex vi is the absolute value of the difference between the number of neighbors to the left and right of vi. The problem is also known as the Balanced Vertex Orderin...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 25 September 2020Accepted: 13 2021Published online: 10 February 2022Keywordsparameterized algorithms, graph theory, width parameter, decomposition, cops and robber gameAMS Subject Headings05C85Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Socie...

Given a graph G and integers k1, k2, and k3, the unit interval editing problem asks whether G can be transformed into a unit interval graph by at most k1 vertex deletions, k2 edge deletions, and k3 edge additions. We give an algorithm solving this problem in time 2 logk) · (n+m), where k := k1 +k2 +k3, and n,m denote respectively the numbers of vertices and edges of G. Therefore, it is fixed-pa...

Today’s SAT solvers have an enormous importance and impact in many practical settings. They are used as efficient back-end to solve many NP-complete problems. However, many computational problems are located at the second level of the Polynomial Hierarchy or even higher, and hence polynomial-time transformations to SAT are not possible, unless the hierarchy collapses. In certain cases one can b...