Combinatorial optimization encompasses a wide range of important computational tasks such as UNIFORMSPARSESTCUT (also known as NORMALIZEDCUT), MAXCUT, TRAVELINGSALESMANPROBLEM, and VERTEXCOVER. Most combinatorial optimization problems are NP-hard to be solved optimally. On one hand, a natural way to cope with this computational intractability is via designing approximation algorithms to efficie...

This article is concerned with the approximation of unbounded convex sets by polyhedra. While there an abundance literature investigating this task for compact sets, results on case are scarce. We first point out connections between existing before introducing a new notion polyhedral called ($\varepsilon,\delta$)-approximation that integrates in meaningful way. Some basic about ($\varepsilon,\d...

For the optimal approximation of convex bodies by inscribed or circumscribed polytopes there are precise asymptotic results with respect to different notions of distance. In this paper we want to derive some results on optimal approximation without restricting the polytopes to be inscribed or circumscribed. Let Pn and P(n) denote the set of polytopes with at most n vertices and n facets, respec...

The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O(n+ k) time, where k is the approximation error control parameter. The proposed algorithm is suitable for applications prefe...

We study joint chance constrained programs (JCCPs). JCCPs are often non-convex and non-smooth, and thus are generally challenging to solve. In this paper, we propose a logarithmsum-exponential smoothing technique to approximate a joint chance constraint by the difference of two smooth convex functions and use a sequential convex approximation algorithm, coupled with a Monte Carlo method, to sol...

Inorder to enhance the capacity and output of a downlink orthogonal frequency division multiple access(OFDMA) network, it is essential to perform appropriate resource allocation. Correct resource allocation suggests that finding best subchannel and power allocation for each and every user. Therefore here associate algorithm is proposed to attain this. Initial of all sub-channel allocation is pe...

We present fast approximation algorithms for the problem of dividing a given convex geographic region into smaller sub-regions so as to distribute the workloads of a set of vehicles. Our objective is to partition the region in such a fashion as to ensure that vehicles are capable of communicating with one another under limited communication radii. We consider variations of this problem in which...