Molecular dissection of dual pseudosymmetric solute translocation pathways in human

Abstract 250 words Introduction 749 word

Simple but Efficient Approaches for the Collapsing Knapsack Problem

AbstractThe collapsing knapsack problem is a generalization of the ordinary knapsack problem, where the knapsack capacity is a non-increasing function of the number of items included. Whereas previous papers on the topic have applied quite involved techniques, the current paper presents and analyzes two rather simple approaches: One approach that is based on the reduction to a standard knapsack problem, and another approach that is based on a simple dynamic programming recursion. Both algorithms have pseudo-polynomial solution times, guaranteeing reasonable solution times for moderate coefficient sizes. Computational experiments are provided to expose the efficiency of the two approaches compared to previous algorithms

SOME GEOMETRIC CLUSTERING PROBLEMS

This paper investigates the computational complexity of several clustering problems with special objective functions for point sets in the Euclidean plane. Our strongest negative result is that clustering a set of 3k points in the plane into k triangles with minimum total circumference is NP-hard. On the other hand, we identify several special cases that are solvable in polynomial time due to the special structure of their optimal solutions: The clustering of points on a convex hull into triangles; the clustering into equal–sized subsets of points on a line or on a circle with special objective functions; the clustering with minimal clusterdistances. Furthermore, we investigate clustering of planar point sets into convex quadrilaterals

Monge Matrices Make Maximization Manageable

We continue the research on the effects of Monge structures in the area of combinatorial optimization. We show that three optimization problems become easy if the underlying cost matrix fulfills the Monge property: (A) The balanced max--cut problem, (B) the problem of computing minimum weight binary k-matchings and (C) the computation of longest paths in bipartite, edge-weighted graphs. In all three results, we first prove that the Monge structure imposes some special combinatorial property on the structure of the optimum solution, and then we exploit this combinatorial property to derive efficient algorithms

Combinatorial optimization problems with conflict graphs

Conflict graphs impose disjunctive constraints for pairs of jobs, items, edges or other objects in a combinatorial optimization problem. Equivalently, the feasible domain of the considered problem is restricted to stable sets in the given conflict graph. After reviewing in our presentation results from the literature for bin packing and scheduling problems with conflict graphs, we first consider the classical 0-1 knapsack problem. Adding a conflict graph makes the problem strongly NP-hard but for three special graph classes, namely trees, graphs with bounded treewidth and chordal graphs, we can develop pseudopolynomial algorithms. From these we can easily derive fully polynomial time approximation schemes (FPTAS). Secondly, we study the minimum spanning tree problem and show that the border between polynomially solvable and NP-hard is given by moving from a conflict graph containing only isolated edges to paths of length 2