A close relation between the optimal packing of spheres in Rd and minimal energy E (effective conductivity) composites with ideally conducting spherical inclusions is established. The location optimal-design problem yields inclusions. geometrical-packing physical-conductivity problems are stated a periodic toroidal d-dimensional space an arbitrarily fixed number n nonoverlapping per periodicity...

Abstract Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features crystalline as well random, irregular two-dimensional (2D) packing structures known. The 2D crosses does not yet belong to category solved problems. We demonstrate experiments different aspect ratios (arm width length) which fractions actually achieved by random p...

The role of the friction coefficient, m, on the jamming properties of disordered, particle packings is studied using computer simulations. Compressed, soft-sphere packings are brought towards the jamming transition—the point where a packing loses mechanical stability—by decreasing the packing fraction. The values of the packing fraction at the jamming transition, fmc, gradually decrease from th...

Obtaining general relations between macroscopic properties of random assemblies, such as density, and the microscopic properties of their constituent particles, such as shape, is a foundational challenge in the study of amorphous materials. By leveraging existing understanding of the random packing of spherical particles, we estimate the random packing density for all sufficiently spherical sha...

Best t is the best known algorithm for on line bin packing in the sense that no algorithm is known to behave better both in the worst case and in the average uniform case In practice Best t appears to perform within a few percent of optimal In this paper we study the expected performance ratio taking the worst case multiset of items L and assuming that the elements of L are inserted in random o...

Random sampling is a powerful tool for gathering information about a group by considering only a small part of it. We discuss some broadly applicable paradigms for using random sampling in combinatorial optimization, and demonstrate the eeectiveness of these paradigms for two optimization problems on matroids: nding an optimum matroid basis and packing disjoint matroid bases. Applications of th...