Linear Time Split Decomposition Revisited

Linear Time Split Decomposition Revisited

Given a family F of subsets of a ground set V , its orthogonal is de ned to be the family of subsets that do not overlap any element of F . Using this tool we revisit the problem of designing a simple linear time algorithm for undirected graph split (also known as 1-join) decomposition.

A Simple Linear Time Split Decomposition Algorithm of Undirected Graphs

We revisit the problem of designing a linear time algorithm for undirected graph split decomposition. Although that this problem has already been claimed to be solved in [E. Dahlhaus, FSTTCS, 1994] and [E. Dahlhaus, Journal of Algorithms 36(2):205-240, 2000], we present a new well founded theoretical background for split decomposition that allow us to clearly design and proove the rst simple li...

Simple, linear-time modular decomposition

Modular decomposition is fundamental for many important problems in algorithmic graph theory including transitive orientation, the recognition of several classes of graphs, and certain combinatorial optimization problems. Accordingly, there has been a drive towards a practical, linear-time algorithm for the problem. Despite considerable effort, such an algorithm has remained elusive. The linear...

The Split Brain Revisited

SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS WITH LINEAR MEMBERSHIP FUNCTIONS-REVISITED

Recently, Gasimov and Yenilmez proposed an approach for solving two kinds of fuzzy linear programming (FLP) problems. Through the approach, each FLP problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. Then, the crisp problem is solved by the use of the modified subgradient method. In this paper we will have another look at the earlier defuzzifi...