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...

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...

The problem of maintaining an approximate solution for one-dimensional bin packing when items may arrive and depart dynamically is studied. In accordance with various work on fully dynamic algorithms, and in contrast to prior work on bin packing, it is assumed that the packing may be arbitrarily rearranged to accommodate arriving and departing items. In this context our main result is a fully d...

Usually, for bin packing problems, we try to minimize the number of bins used or in the case of the dual bin packing problem, maximize the number or total size of accepted items. This paper presents results for the opposite problems, where we would like to maximize the number of bins used or minimize the number or total size of accepted items. We consider off-line and on-line variants of the pr...

We study pseudo-polynomial Strip Packing. Given a set of rectangular axis parallel items and a strip with bounded width and infinite height the objective is to find a packing of the items into the strip which minimizes the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. It is known ...

The dense packing observed in protein interiors appears to be crucial for stabilizing the native structure--even subtle internal substitutions are usually destabilizing. Thus, steric complementarity of core residues is thought to be an important criterion for "inverse folding" predictive methods, which judge whether a newly determined sequence is consistent with any known folds. A major problem...

We consider (closed neighbourhood) packings and their generalization in graphs called limited packings. A vertex set X in a graphG is a k-limited packing if for any vertex v ∈ V (G), |N [v] ∩X | ≤ k, where N [v] is the closed neighbourhood of v. The k-limited packing number Lk(G) is the largest size of a k-limited packing in G. Limited packing problems can be considered as secure facility locat...

We present approximation algorithms for the orthogonal z-oriented three-dimensional packing problem (TPPz) and analyze their asymptotic performance bound. This problem consists in packing a list of rectangular boxes L = (b1, b2, . . . , bn) into a rectangular box B = (l, w,∞), orthogonally and oriented in the z-axis, in such a way that the height of the packing is minimized. We say that a packi...

We consider three problems about cities from Alcuin’s Propositiones ad acuendos juvenes. These problems can be considered as the earliest packing problems difficult also for modern state-of-the-art packing algorithms. We discuss the Alcuin’s solutions and give the known (to the author) best solutions to these problems.

We propose exact algorithms for the 2-dimensional strip packing problem (2SP) with and without 90 degrees rotations. We first focus on the perfect packing problem (PP), which is a special case of 2SP, wherein all given rectangles are required to be packed without wasted space, and design branch-and-bound algorithms introducing several branching rules and bounding operations. A combination of th...