Approximation algorithm for the partial set multi-cover problem

the algorithm for solving the inverse numerical range problem

برد عددی ماتریس مربعی a را با w(a) نشان داده و به این صورت تعریف می کنیم w(a)={x8ax:x ?s1} ، که در آن s1 گوی واحد است. در سال 2009، راسل کاردن مساله برد عددی معکوس را به این صورت مطرح کرده است : برای نقطه z?w(a)، بردار x?s1 را به گونه ای می یابیم که z=x*ax، در این پایان نامه ، الگوریتمی برای حل مساله برد عددی معکوس ارانه می دهیم.

Packing-Based Approximation Algorithm for the k-Set Cover Problem

We present a packing-based approximation algorithm for the k-Set Cover problem. We introduce a new local search-based k-set packing heuristic, and call it Restricted k-Set Packing. We analyze its tight approximation ratio via a complicated combinatorial argument. Equipped with the Restricted k-Set Packing algorithm, our k-Set Cover algorithm is composed of the k-Set Packing heuristic [7] for k ...

An Approximation Algorithm for the Minimum Latency Set Cover Problem

The input to the minimum latency set cover problem (MLSC) consists of a set of jobs and a set of tools. Each job j needs a specific subset Sj of the tools in order to be processed. It is possible to install a single tool in every time unit. Once the entire subset Sj has been installed, job j can be processed instantly. The problem is to determine an order of job installations which minimizes th...

Improved Approximation Algorithms for the Partial Vertex Cover Problem

A Better-Than-Greedy Approximation Algorithm for the Minimum Set Cover Problem

In the weighted set-cover problem we are given a set of elements E = {e1, e2, . . . , en} and a collection F of subsets of E, where each S ∈F has a positive cost cS . The problem is to compute a sub-collection SOL such that ⋃ S∈SOL Sj = E and its cost ∑ S∈SOL cS is minimized. When |S| ≤ k ∀S ∈ F we obtain the weighted k-set cover problem. It is well known that the greedy algorithm is an Hk-appr...