On the fractionality of the path packing problem

On fractionality of the path packing problem

Given an undirected graph G = (N,E), a subset T of its nodes and an undirected graph (T, S), G and (T, S) together are often called a network. A collection of paths in G whose end-pairs lie in S is called an integer multiflow. When these paths are allowed to have fractional weight, under the constraint that the total weight of the paths traversing a single edge does not exceed 1, we have a frac...

 Abstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...

Bounded fractionality of the multiflow feasibility problem for demand graph K 3 + K 3 and related

We consider the multiflow feasibility problem whose demand graph is the vertex-disjoint union of two triangles. We show that this problem has a 1/12-integral solution or no solution under the Euler condition. This solves a conjecture raised by Karzanov, and completes the classification of the demand graphs having bounded fractionality. We reduce this problem to the multiflow maximization proble...

A Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

Bounded fractionality of the multiflow feasibility problem for demand graph K3+K3 and related maximization problems

We consider the multiflow feasibility problem whose demand graph is the vertexdisjoint union of two triangles. We show that this problem has a 1/12-integral solution whenever it is feasible and satisfies the Euler condition. This solves a conjecture raised by Karzanov, and completes the classification of the demand graphs having bounded fractionality. We reduce this problem to the multiflow max...