Publication

Node disjoint paths of minimum total lenght on 2-trees

Thomas Liebling
1988
Reports

Abstract

The problem of finding p(and even 2) node disjoint paths on a digraph, connecting p pair of terminals is NP-complete. For directed k-trees however, the problem is polynomial. In this paper, we give a linear algorithm for the corresponding optimisation problem on 2-trees and for the case p=2, we characterize te convex hull of the corresponding edge incidence vectors. The optimization algorithm ramains linear and independent of p for k > or equal 3 if the terminals are distinct

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Thomas Liebling
1988
Reports

Abstract

Official source

Related concepts (31)

Binary tree

In computer science, a binary tree is a k-ary tree data structure in which each node has at most two children, which are referred to as the and the . A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (L, S, R), where L and R are binary trees or the empty set and S is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences.

Red–black tree

In computer science, a red–black tree is a specialised binary search tree data structure noted for fast storage and retrieval of ordered information, and a guarantee that operations will complete within a known time. Compared to other self-balancing binary search trees, the nodes in a red-black tree hold an extra bit called "color" representing "red" and "black" which is used when re-organising the tree to ensure that it is always approximately balanced.

Directed graph

In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs. In formal terms, a directed graph is an ordered pair where V is a set whose elements are called vertices, nodes, or points; A is a set of ordered pairs of vertices, called arcs, directed edges (sometimes simply edges with the corresponding set named E instead of A), arrows, or directed lines.

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