We present a linear time algorithm for the minimum linear arrangement problem on proper interval graphs. The obtained ordering is a 4-approximation for general interval graphs. 1 Preliminaries Let F be a family of nonempty sets. The intersection graph of F is obtained by representing each set in F by a vertex and connecting two vertices by an edge if and only if their corresponding sets interse...

This paper presents a hybrid genetic algorithm for the minimum linear arrangement problem. The algorithm was tested on a collection of 22 sparse graphs that has been used to test twelve other algorithms for the minimum linear arrangement problem. The graphs have up to 10,240 vertices and up to 49,820 edges. On about 2/3 of the graphs, our algorithm found solutions superior to all other algorith...

Finding a linear ordering of the vertices of a graph is a common problem arising in diverse applications. In this paper we present a linear-time algorithm for this problem, based on the multi-scale paradigm. Experimental results are similar to those of the best known approaches, while the running time is significantly better, enabling it to deal with much larger graphs. The paper contains a gen...

We observe that combining the techniques of Arora, Rao, and Vazirani, with the rounding algorithm of Rao and Richa yields an O( √ log n log log n)-approximation for the minimum-linear arrangement problem. This improves over the O(log n)-approximation of Rao and Richa.

Let V be a linear space of dimension over a field K. By an arrangement we shall mean a finite collection of affine subspaces of V . If all of the subspaces in an arrangement A have codimension k then we say that A is an ( , k)arrangement. If k = 1 and so A is a hyperplane arrangement then we shall say that A is an -arrangement. Let A be an arrangement and S the coordinate ring for V . For each ...

Two algorithms for minimum cut linear arrangement of a class of graphs called p-q dags are proposed. A p-q dag represents the connection scheme of an adder tree, such as Wallace tree, and the VLSI layout problem of a bit slice of an adder tree is treated as the minimum cut linear arrangement problem of its corresponding p-q dag. One of the two algorithms is based on dynamic programming. It calc...

Let G = (V0; V1 ; V2; E) be a 3-layer graph. The 3-layer drawings of G in which V0 , V1 , and V2 are placed on 3 parallel lines and each edge in E is drawn using one straight line segment, are studied. A generalization of the linear arrangement problem which we call the 3-layer pseudo linear arrangement problem is introduced, and it is shown to be closely related to the 3-layer crossing number....

We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a com-binatorial construction (blocker duality) which yields such generators in cases with a lot of combinatorial structure, and we present the examples that motivated our work. We give a construction which produces al...

We consider the vanishing ideal of an arrangement of linear subspaces in a vector space and investigate when this ideal can be generated by products of linear forms. We introduce a combinatorial construction (blocker duality) which yields such generators in cases with a lot of combinatorial structure, and we present the examples that motivated our work. We give a construction which produces all...