Min-Sum Set Cover and Its Generalizations

Some remarks on generalizations of classical prime submodules

Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. Suppose that $phi:S(M)rightarrow S(M)cup lbraceemptysetrbrace$ be a function where $S(M)$ is the set of all submodules of $M$. A proper submodule $N$ of $M$ is called an $(n-1, n)$-$phi$-classical prime submodule, if whenever $r_{1},ldots,r_{n-1}in R$ and $min M$ with $r_{1}ldots r_{n-1}min Nsetminusphi(N)$, then $r_{1...

Results on the min-sum vertex cover problem

Let G be a graph with the vertex set V (G), edge set E(G). A vertex labeling is a bijection f : V (G)→ {1, 2, . . . , |V (G)|}. The weight of e = uv ∈ E(G) is given by g(e) = min{f(u), f(v)}. The min-sum vertex cover (msvc) is a vertex labeling that minimizes the vertex cover number μs(G) = ∑ e∈E(G) g(e). The minimum such sum is called the msvc cost. In this paper, we give both general bounds a...

A note on the generalized min-sum set cover problem

In this paper, we consider the generalized min-sum set cover problem, introduced by Azar, Gamzu, and Yin [1]. Bansal, Gupta, and Krishnaswamy [2] give a 485approximation algorithm for the problem. We are able to alter their algorithm and analysis to obtain a 28-approximation algorithm, improving the performance guarantee by an order of magnitude. We use concepts from α-point scheduling to obtai...

Primal-Dual RNC Approximation Algorithms for Set Cover and Covering Integer Programs

We build on the classical greedy sequential set cover algorithm, in the spirit of the primal-dual schema, to obtain simple parallel approximation algorithms for the set cover problem and its generalizations. Our algorithms use randomization, and our randomized voting lemmas may be of independent interest. Fast parallel approximation algorithms were known before for set cover, though not for the...

Approximating Min - sum Set Cover 1 Uriel