Metric packing for K 3 + K 3 Hiroshi HIRAI

Metric packing for K 3 + K 3 Hiroshi HIRAI Research Institute for

In this paper, we consider the metric packing problem for the commodity graph of disjoint two triangles K3 +K3, which is dual to the multiflow feasibility problem for the commodity graph K3 + K3. We prove Karzanov’s conjecture concerning quarter-integral packings by certain bipartite metrics.

Metric packing for K3+K3

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 moment based metric for 2-D and 3-D packing

The most common metric used today to evaluate the effectiveness of a packing technique is the percentage of space used. An inherent limitation of this metric is its inability to differentiate between two different packing arrangements of the same set of objects. This paper proposes an alternative metric for both the 2D and 3D cases, called the point moment metric, and expands on the theory behi...

Improved Lower Bounds for the Online Bin Packing Problem with Cardinality Constraints

The bin packing problem has been extensively studied and numerous variants have been considered. The k-item bin packing problem is one of the variants introduced by Krause et al. in Journal of the ACM 22(4). In addition to the formulation of the classical bin packing problem, this problem imposes a cardinality constraint that the number of items packed into each bin must be at most k. For the o...