A solution to the three disjoint path problem on honeycomb tori

In a previous paper we solved an open problem named as the three disjoint path problem on honeycomb meshes. In this paper we extend the technique used to solve the related problem on honeycomb tori. The result gives the minimum possible length of the longest of any three disjoint paths between two given nodes in a torus. The problem has practical benefits in the fault tolerant aspects of interconnection topologies.

A solution to the three disjoint path problem on honeycomb meshes

Recently honeycomb meshes have been considered as alternative candidates for interconnection networks in parallel and distributed computer systems. This paper presents a solution to one of the open problems about honeycomb meshes—the so-called three disjoint path problem. The problem requires minimizing the length of the longest of any three disjoint paths between 3-degree nodes. This solution provides information on the re-routing of traffic along the network in the presence of faults.

Adaptive-threshold region merging via path scanning

Region merging algorithms commonly produce results that are seen to be far below the current commonly accepted state-of-the-art image segmentation techniques. The main challenging problem is the selection of an appropriate and computationally efficient method to control resolution and region homogeneity. In this paper we present a region merging algorithm that includes a semi-greedy criterion and an adaptive threshold to control segmentation resolution. In addition we present a new relative performance indicator that compares algorithm performance across many metrics against the results from human segmentation. Qualitative (visual) comparison demonstrates that our method produces results that outperform existing leading techniques.