Permutation algorithms on optical multi-trees

The permutation-path coloring problem on trees

In this paper we rst show that the permutation-path coloring problem is NP-hard even for very restrictive instances like involutions, which are permutations that contain only cycles of length at most two, on both binary trees and on trees having only two vertices with degree greater than two, and for circular permutations which are permutations that contain exactly one cycle on trees with maxim...

On random trees obtained from permutation graphs

A permutation w gives rise to a graph Gw; the vertices of Gw are the letters in the permutation and the edges of Gw are the inversions of w. We find that the number of trees among permutation graphs with n vertices is 2n−2 for n ≥ 2. We then study Tn, a uniformly random tree from this set of trees. In particular, we study the number of vertices of a given degree in Tn, the maximum degree in Tn,...

Computational Geometry on Optical Multi-Trees (OMULT) Computer System

This paper presents simple and efficient algorithms for fundamental computational geometry problems on OMULT (Optical Multi-Trees) system [5] that uses both electronic and optical links among processors. We show that the algorithms for convex hull and the smallest enclosing box can be computed on this network in O(log n) time, compared to O( √ n) algorithms on the OTISMesh[6] for each of these ...

Algorithms on Phylogenetic Trees

Permutation Generation: Two New Permutation Algorithms

Two completely new algorithms for generating permutations–shift cursor algorithm and level algorithm–and their efficient implementations are presented in this paper. One implementation of shift cursor algorithm gives an optimal solution of permutation generation problem, and one implementation of level algorithm can be used to generate random permutations.