the set covering problem (scp) is a well-known combinatorial optimization problem. this paper investigates development of a local branching approach for the scp. this solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. the algorithm parameters are tuned by design of experiments approach. the proposed method is te...

Filon quadrature, designed specifically for a common class of oscillatory integrals, is easily implemented in a computer algebra system (CAS) using exact or approximate arithmetic. Although quadrature is almost always used in the context of approximation, we see that various properties are exhibited by running an exact algorithm on exact symbolic inputs. This experimental approach to the mathem...

Motivated by a bus routing application, we study the following rectangle escape problem: Given a set S of n rectangles inside a rectangular region R, extend each rectangle in S toward one of the four borders of R so that the maximum density over the region R is minimized, where the density of each point p ∈ R is defined as the number of extended rectangles containing p. We show that the problem...

In this paper we present a new, query based approach for approximating polygonal chains in the plane. We give a few results based on this approach, some of more general interest, and propose a greedy heuristic to speed up the computation. Our algorithms are simple, based on standard geometric operations, and thus suitable for efficient implementation. We also show that the query based approach ...

We devise a method for designing materials that will have some desired structural characteristics. We apply it to multiblock copolymers that have two different types of monomers, A and B. We show how to determine what sequence of A’s and B’s should be synthesised in order to give a particular structure and morphology. Using this method in conjunction with the theory of microphase separation dev...

In this lecture, the focus is on primal dual method and its application in designing exact algorithms and approximation algorithms for combinatorial optimization problems. It is a general framework which can solve many problems rather systematically. We first introduce the principles of primal dual program, and then show one example, weighted bipartite matching for designing exact algorithm and...

Spanners are sparse subgraphs that preserve distances up to a given factor in the underlying graph. Recently spanners have found important practical applications in metric space searching and message distribution in networks. These applications use some variant of the socalled greedy algorithm for constructing the spanner — an algorithm that mimics Kruskal’s minimum spanning tree algorithm. Gre...

The main bottleneck of the research in metric space searching is the so-called curse of dimensionality, which makes the task of searching some metric spaces intrinsically diicult, whatever algorithm is used. A recent trend to break this bottleneck resorts to probabilistic algorithms , where it has been shown that one can nd 99% of the elements at a fraction of the cost of the exact algorithm. T...

This paper studies the worst-case performance of the successive approximation algorithm for four identical knapsacks. The algorithm packs the knapsacks successively by using an exact algorithm on the remaining items for each single knapsack. We show that it is an 8 11 -approximation algorithm, and the bound is tight.