Triple-loop networks with arbitrarily many minimum distance diagrams

Triple-loop networks with arbitrarily many minimum distance diagrams

Minimum distance diagrams are a way to encode the diameter and routing information of multi-loop networks. For the widely studied case of double-loop networks, it is known that each network has at most two such diagrams and that they have a very definite form (" L-shape "). In contrast, in this paper we show that there are triple-loop networks with an arbitrarily big number of associated minimu...

Measuring Musical Rhythm Similarity: Further Experiments with the Many-to-Many Minimum-Weight Matching Distance

Musical rhythms are represented as sequences of symbols. The sequences may be composed of binary symbols denoting either silent or monophonic sounded pulses, or ternary symbols denoting silent pulses and two types of sounded pulses made up of low-pitched (dum) and high-pitched (tak) sounds. Experiments are described that compare the effectiveness of the many-to-many minimum-weight matching betw...

New dense families of triple loop networks

Multi-loop digraphs are widely studied mainly because of their symmetric properties and their applications to loop networks. A multi-loop digraph G=G(N;s~,...,SA) has set of vertices V-ZN and adjacencies given by v ~ v + si modN, i = 1 ..... A. For every fixed N, an usual extremal problem is to find the minimum value D(N) = min D(N; where D(N;s~ ..... s~) is the diameter of G. A closely related...

Many-to-Many Disjoint Path Covers in Double Loop Networks

The minimum distance diagram and diameter of undirected double-loop networks

This thesis proposes a minimum distance diagram of undirected double-loop, which makes use of the cyclic graph's excellent properties on the node number and path length to achieve high performance. Main issues include the method to build the minimum distance diagram of undirected double-loop networks, the algorithm to calculate its diameter, and the step to build optimal undirected double-loop ...