Rafael Crivellari Saliba Schouery

Polynomial-Time Approximation Schemes for Circle Packing Problems

We consider the problem of packing a set of circles into a minimum number of unit square bins. We give an asymptotic approximation scheme (APTAS) when we have resource augmentation in one dimension, that is, we may use bins of height 1 + γ, for some small γ > 0. As a corollary, we also obtain an APTAS for the circle strip packing problem, whose objective is to pack a set of circles into a strip of unit width and minimum height. These are the first approximation schemes for these problems. Our algorithm is based on novel ideas of iteratively separating small and large items, and may be extended to more general packing problems. For example, we also obtain APTAS’s for the corresponding problems of packing d-dimensional spheres under the L p -norm.

A bounded space algorithm for online circle packing

We study the Online Circle Packing Problem where we need to pack circles that arrive online in square bins with the objective to minimize the number of bins used. An online algorithm is said to have bounded space if at any given time, only a constant number of bins are open, circles are packed only in open bins and once a bin is closed it cannot be reopened. In particular, we present a 2.4394-competitive bounded space algorithm for this problem and a 2.2920 lower bound on the competitive ratio of any online bounded space algorithm for this problem. We present results for the Online Circle Packing Problem.A 2.4394-competitive bounded space algorithm.A 2.292 lower bound on the competitive ratio of any online bounded space algorithm.We combine Integer Linear Programming with Constraint Programming for computations.

Polynomial-Time Approximation Schemes for Circle and Other Packing Problems

We consider the problem of packing a set of circles into a minimum number of unit square bins. To obtain rational solutions, we use augmented bins of height

Approximation Algorithms for the Max-Buying Problem with Limited Supply

1+\gamma

The Envy-Free Pricing Problem and Unit-Demand Markets

1+γ, for some arbitrarily small number

A Continuous Enhancement Routing Solution aware of data aggregation for Wireless Sensor Networks

\gamma > 0