HOMOTOPY BASE OF ACYCLIC GRAPHS - A COMBINATORIAL ANALYSIS OF COMMUTATIVE DIAGRAMS BY MEANS OF PREORDERED MATROID

被引：1

作者：

MUROTA, K

机构：

[1] Univ of Tokyo, Tokyo, Jpn, Univ of Tokyo, Tokyo, Jpn

来源：

DISCRETE APPLIED MATHEMATICS | 1987年 / 17卷 / 1-2期

关键词：

COMPUTER PROGRAMMING - Algorithms;

D O I：

10.1016/0166-218X(87)90009-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A diagram is an acyclic graph with (linear) maps associated with arcs. The problem considered is which set of relations characterizes the commutativity of a given diagram and how to find such a set of relations. The dependence among parallel paths of an acyclic graph is analyzed by means of 'preordered matroid', which is a composite algebraic structure of preorder and matroid. The notation of 'homotopy base' is introduced; any two bases are shown to be equicardinal, and a base can be found by an efficient greedy elimination algorithm, which, starting with a spanning set, deletes dependent elements one by one in an arbitrary order.

引用

页码：135 / 155

页数：21