In a typical covering problem we are given a universe U of size n, a family S (S could be given implicitly) of sizem and an integer k and the objective is to check whether there exists a subfamily S ′ ⊆ S of size at most k satisfying some desired properties. If S ′ is required to contain all the elements of U then it corresponds to the classical Set Cover problem. On the other hand if we requir...

An infeasible interior-point algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and Nesterov-Todd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interior-point ...

the topological index of a graph g is a numeric quantity related to g which is invariant underautomorphisms of g. the vertex pi polynomial is defined as piv (g)  euv nu (e)  nv (e).then omega polynomial (g,x) for counting qoc strips in g is defined as (g,x) =cm(g,c)xc with m(g,c) being the number of strips of length c. in this paper, a new infiniteclass of fullerenes is constructed. the ...

We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order r increases and (b) there exist probability measures such that the moment relaxation is equivalent to the or...

Geometric covering is a well-studied topic in computational geometry. We study three covering problems: Disjoint Unit-Disk Cover, Depth-(≤ K) Packing and Red-Blue UnitSquare Cover. In the Disjoint Unit-Disk Cover problem, we are given a point set and want to cover the maximum number of points using disjoint unit disks. We prove that the problem is NP-complete and give a polynomial-time approxim...

In the bin covering problem there is a group L=(a1; : : : ; an) of items with sizes s̃(ai)∈ (0; 1), and the goal is to 6nd a packing of the items into bins to maximize the number of bins that receive items of total size at least 1. This is a dual problem to the classical bin packing problem. In this paper we present the 6rst asymptotic fully polynomial-time approximation scheme for the problem. ...