Related papers: Efficient algorithms for the dense packing of cong…
We provide a tight result for a fundamental problem arising from packing disks into a circular container: The critical density of packing disks in a disk is 0.5. This implies that any set of (not necessarily equal) disks of total area…
The article demonstrates rather general approach to problems of discrete geometry: treat them as global optimization problems to be solved by one of general purpose solver implementing branch-and-bound algorithm (B&B). This approach may be…
In this work we propose algorithms to explicitly construct a conservative estimate of the configuration spaces of rigid objects in 2D and 3D. Our approach is able to detect compact path components and narrow passages in configuration space…
Given a point set $S=\{s_1,\ldots , s_n\}$ in the unit square $U=[0,1]^2$, an anchored square packing is a set of $n$ interior-disjoint empty squares in $U$ such that $s_i$ is a corner of the $i$th square. The reach $R(S)$ of $S$ is the set…
Studies of random close packing of spheres have advanced our knowledge about the structure of systems such as liquids, glasses, emulsions, granular media, and amorphous solids. When these systems are confined their structural properties…
We consider stochastic settings for clustering, and develop provably-good approximation algorithms for a number of these notions. These algorithms yield better approximation ratios compared to the usual deterministic clustering setting.…
Let $S$ be a set of $n$ points in the unit square $[0,1]^2$, one of which is the origin. We construct $n$ pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in $S$, and the…
The Two-dimensional Bin Packing Problem calls for packing a set of rectangular items into a minimal set of larger rectangular bins. Items must be packed with their edges parallel to the borders of the bins, cannot be rotated and cannot…
We consider the irregular strip packing problem of rasterized shapes, where a given set of pieces of irregular shapes represented in pixels should be placed into a rectangular container without overlap. The rasterized shapes provide simple…
High-dimensional simulation optimization is notoriously challenging. We propose a new sampling algorithm that converges to a global optimal solution and suffers minimally from the curse of dimensionality. The algorithm consists of two…
As the main problem, we consider covering of a $d$-dimensional cube by $n$ balls with reasonably large $d$ (10 or more) and reasonably small $n$, like $n=100$ or $n=1000$. We do not require the full coverage but only 90\% or 95\% coverage.…
We study the design of interactive clustering algorithms for data sets satisfying natural stability assumptions. Our algorithms start with any initial clustering and only make local changes in each step; both are desirable features in many…
Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items,…
The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from…
Finding the product of two polynomials is an essential and basic problem in computer algebra. While most previous results have focused on the worst-case complexity, we instead employ the technique of adaptive analysis to give an improvement…
We consider the problem of grouping items into clusters based on few random pairwise comparisons between the items. We introduce three closely related algorithms for this task: a belief propagation algorithm approximating the Bayes optimal…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
Consider a set $P$ of $n$ points on the boundary of an axis-aligned square $Q$. We study the boundary-anchored packing problem on $P$ in which the goal is to find a set of interior-disjoint axis-aligned rectangles in $Q$ such that each…
We apply a recent one-dimensional algorithm for predicting random close packing fractions of polydisperse hard spheres [Farr and Groot, J. Chem. Phys. 133, 244104 (2009)] to the case of lognormal distributions of sphere sizes and mixtures…
This paper considers the problem of finding maximum volume (axis-aligned) inscribed boxes in a compact convex set, defined by a finite number of convex inequalities, and presents optimization and geometric approaches for solving them.…