Sentence examples for minimum vertex cover from inspiring English sources

We exemplify this idea by designing and analysing parameterised approximation algorithms for minimum vertex cover.

An FPT algorithm is also proposed which considers as a parameter the size of the minimum vertex cover.

The Minimum Vertex Cover (MVC) problem is a well-known combinatorial optimization problem of great importance in theory and applications.

For a given graph G over n vertices, let OPTG denote the size of an optimal solution in G of a particular minimization problem (e.g., the size of a minimum vertex cover).

In particular, for l="1 (factor-1.5 approximation) our algorithm runs in time O∗(1.0883k), where parameter k≤23τ, and τ is the size of a minimum vertex cover.

The minimum weighted vertex cover (MWVC) problem, an extension of the classical minimum vertex cover (MVC) problem, is an important NP-complete combinatorial optimization problem with a wide range of applications.

For weighted König-Egerváry graphs (G,w) we observe that the set of vertices belonging to all minimum vertex covers, and the set of vertices belonging to no minimum vertex covers, can be efficiently computed.

Chen and Jost [3] established the relationship between minimum vertex covers and the eigenvalues of the normalized Laplacian on trees.

Proposition 1. Finding a minimum-weight vertex cover in the conflict graph G c(T, P) one-to-one corresponds to determining a minimum-weight set of pairs that cannot be satisfied in (T, P).

Due to Proposition 1 we can immediately conclude that MTO and W-MTO are fixed-parameter tractable with respect to the parameter "number of pairs" p, since the conflict graph has p vertices and we can find a minimum-weight vertex cover by trying all possibilities in 2 p ⋅ n O(1) time.

Further, since minimum-weight vertex covers can be found in O(1.379 k+ kn) time [ 16], we have fixed-parameter tractability with respect to the parameter "number of unsatisfied pairs", and if all weights are at least one, also with respect to the parameter "total weight of unsatisfied pairs".