Pseudo-polynomial time algorithms for combinatorial food mixture packing problems

Combinatorial algorithms for packing and scheduling problems

Improved Pseudo-Polynomial-Time Approximation for Strip Packing

We study the strip packing problem, a classical packing problem which generalizes both bin packing and makespan minimization. Here we are given a set of axis-parallel rectangles in the two-dimensional plane and the goal is to pack them in a vertical strip of fixed width such that the height of the obtained packing is minimized. The packing must be non-overlapping and the rectangles cannot be ro...

Polynomial Time Algorithms for Bichromatic Problems

In this article, we consider a collection of geometric problems involving points colored by two colors (red and blue), referred to as bichromatic problems. The motivation behind studying these problems is two fold; (i) these problems appear naturally and frequently in the fields like Machine learning, Data mining, and so on, and (ii) we are interested in extending the algorithms and techniques ...

Polynomial-Time Algorithms for Phylogenetic Inference Problems

A common problem in phylogenetics is to try to infer a species phylogeny from gene trees. We consider different variants of this problem. The first variant, called Unrestricted Minimal Episodes Inference, aims at inferring a species tree based on a model of speciation and duplication where duplications are clustered in duplication episodes. The goal is to minimize the number of such episodes. T...

Polynomial Time Approximation Schemes for Class-Constrained Packing Problems

We consider variants of the classic bin packing and multiple knapsack problems, in which sets of items of di erent classes (colours) need to be placed in bins; the items may have di<erent sizes and values. Each bin has a limited capacity, and a bound on the number of distinct classes of items it can accommodate. In the class-constrained multiple knapsack (CCMK) problem, our goal is to maximize ...