We consider the problem of packing a family of disks “on a shelf,” that is, such that each disk touches the x-axis from above and such that no two disks overlap. We prove that the problem of minimizing the distance between the leftmost point and the rightmost point of any disk is NP-hard. On the positive side, we show how to approximate this problem within a factor of 4/3 in O(n logn) time, and...

We study in this paper a new channel pin assignment problem for the new cell model in which all the pins are positioned along a horizontal line inside their corresponding cells. An exact algorithm is presented, and its application to over-the-cell routing is also addressed.

Recently, Waldmann considered an algorithm to compute the aggregate claims distribution in the individual life model which is an efficient reformulation of the original exact algorithm of De Pril. In this paper we will show that in practice the approximations as proposed by De Pril are still more efficient than the exact algorithm of Waldmann both in terms of the number of computations required...

In this paper, we will introduce an exact algorithm with a time complexity of O(1.299) for the weighted mutually exclusive set cover problem, where m is the number of subsets in the problem. This problem has important applications in recognizing mutation genes that cause different cancer diseases.

We describe a new algorithm for computing a Nash equilibrium in graphical games, a compact representation for multi-agent systems that we introduced in previous work. The algorithm is the first to compute equilibria both efficiently and exactly for a non-trivial class of graphical games.

Gene annotation databases (compendiums maintained by the scientific community that describe the biological functions performed by individual genes) are commonly used to evaluate the functional properties of experimentally derived gene sets. Overlap statistics, such as Fishers Exact test (FET), are often employed to assess these associations, but don't account for non-uniformity in the number of...

In this paper we merge recent developments on exact algorithms for finding an ordering of vertices of a given graph that minimizes bandwidth (the BANDWIDTH problem) and for finding an embedding of a given graph into a line that minimizes distortion (the DISTORTION problem). For both problems we develop algorithms that work in O(9.363) time and polynomial space. For BANDWIDTH, this improves O(10...

Python implementation of Algorithm X by Knuth is presented. Algorithm X finds all solutions to the exact cover problem. The exemplary results for pentominoes, Latin squares and Sudoku are given.

A hidden guard set G is a set of point guards in polygon P that all points of the polygon are visible from some guards in G under the constraint that no two guards may see each other. In this paper, we consider the problem for finding minimum hidden guard sets in histogram polygons under orthogonal visibility. Two points p and q are orthogonally visible if the orthogonal bounding rectangle for ...