We use the modular decomposition to give O(n(m + n)) algorithms for finding a maximum weighted clique (respectively stable set) and an approximate weighted colouring (respectively partition into cliques) in a (P5, P5)-free graph. As a by-product, we obtain an O(m+n) algorithm for finding a minimum weighted transversal of the C5 in a (P5, P5)free graph.

background & aim: dbs (deep brain stimulation) is a new and successful technique in treatment of symptoms of parkinsonism especially after drug resistance. research in this field is mostly designed for evolution of this technique. the present study aimed at evaluating the relationship between the angle formed in midsagittal and stn (sub-thalamic nucleus) axis line and recording length in the fi...

The Degree Contractibility problem is to test whether a given graph G can be modified to a graph of minimum degree at least d by using at most k contractions. We prove the following three results. First, Degree Contractibility is NP-complete even when d = 14. Second, it is fixed-parameter tractable when parameterized by k and d. Third, it is W[1]-hard when parameterized by k. We also study its ...

Recently, a variety of clustering algorithms have been proposed to handle data that is not linearly separable. Spectral clustering and kernel k -means are two such methods that are seemingly quite different. In this paper, we show that a general weighted kernel k -means objective is mathematically equivalent to a weighted graph partitioning objective. Special cases of this graph partitioning ob...

In this paper we introduce the incremental assignment problem. In this problem, a new pair of vertices and their incident edges are added to a weighted bipartite graph whose maximum weighted matching is already known, and the maximum weighted matching of the extended graph is sought. We propose an O(|V |2) algorithm for the problem.

We observe that ω(G) + χ(S( G)) = n = ω(S( G)) + χ(G) for any graph G with n vertices, where G is any acyclic orientation of G and where S( G) is the (complement of the) auxiliary line graph introduced in [1]. (Where as usual, ω and χ denote the clique number and the chromatic number.) It follows that, for any graph parameter β(G) sandwiched between ω(G) and χ(G), then Φβ( G) := n−β(S( G)) is s...

Wattenhofer et al. [WW04] derive a complicated distributed algorithm to compute a weighted matching of an arbitrary weighted graph, that is at most a factor 5 away from the maximum weighted matching of that graph. We show that a variant of the obvious sequential greedy algorithm [Pre99], that computes a weighted matching at most a factor 2 away from the maximum, is easily distributed. This yiel...