We use a new approximation measure, the differential approximation ratio, to derive polynomial-time approximation algorithms for minimum set covering (for both weighted and unweighted cases), minimum graph coloring and bin-packing. We also propose differentialapproximation-ratio preserving reductions linking minimum coloring, minimum vertex covering by cliques, minimum edge covering by cliques ...

A graph is called pseudo-outerplanar if each block has an embedding on the plane in such a way that the vertices lie on a fixed circle and the edges lie inside the disk of this circle with each of them crossing at most one another. In this paper, we prove that each pseudo-outerplanar graph admits edge decompositions into a linear forest and an outerplanar graph, or a star forest and an outerpla...

This paper addresses a version of the single-facility Maximal Covering Location Problem on network where demand is: (i) distributed along edges and (ii) uncertain with only known interval estimation. To deal this problem, we propose minmax regret model service facility can be located anywhere network. problem is called Minmax Regret (MMR-EMCLP). Furthermore, present two polynomial algorithms fo...

Let G be a simple graph of order n and size m. An edge covering of the graph G is a set of edges such that every vertex of the graph is incident to at least one edge of the set. Let e(G, k) be the number of edge covering sets of G of size k. The edge cover polynomial of G is the polynomial E(G, x) = m

What is the length of the shortest sequence S of reals so that the set of consecutive n-words in S form a covering code for permutations on {1, 2, . . . , n} of radius R ? (The distance between two n-words is the number of transpositions needed to have the same order type.) The above problem can be viewed as a special case of finding a De Bruijn covering code for a rooted hypergraph. Each edge ...

A graph $G$ contains another $H$ as an immersion if can be obtained from a subgraph of by splitting off edges and removing isolated vertices. In this paper, we prove edge-variant the Erd\H{o}s-P\'{o}sa property with respect to containment in 4-edge-connected graphs. More precisely, that for every $H$, there exists function $f$ such $G$, either $k$ pairwise edge-disjoint subgraphs each containin...

We consider the following problem given a pla nar straight line graph nd a covering triangulation whose maximum angle is as small as possible A cov ering triangulation is a triangulation whose vertex set contains the input vertex set and whose edge set con tains the input edge set The covering triangulation problem di ers from the usual Steiner triangulation problem in that we may not add a ver...

Covering is a widely used form of data structures. Covering-based rough set theory provides a systematic approach to this data. In this paper, graphs are connected with covering-based rough sets. Specifically, we convert some important concepts in graph theory including vertex covers, independent sets, edge covers, and matchings to ones in covering-based rough sets. At the same time, correspond...

Let H be a graph. We show that there exists n0 = n0(H) such that for every n ≥ n0, there is a covering of the edges of Kn with copies of H where every edge is covered at most twice and any two copies intersect in at most one edge. Furthermore, the covering we obtain is asymptotically optimal.