On Optimal Linear Arrangements of Trees

نویسندگان

  • F. R. K. CHUNG
  • Ronald L. Graham
چکیده

Let G be an undirected graph with vertex set V(G) and edge set E(G) (see [2] for undefined graph theory terminology). A linear arrangement n of G is a one-to-one mapping from V(G) to the set of positive integers. The weight of an edge e = {u, u} in a linear arrangement 7c is defined to be the absolute value of z(u) n(v). The cost of the linear arrangement 7~ of G, denoted by J=(C), is defined to be:

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The scaling of the minimum sum of edge lengths in uniformly random trees

The minimum linear arrangement problem on a network consists of finding the minimum sum of edge lengths that can be achieved when the vertices are arranged linearly. Although there are algorithms to solve this problem on trees in polynomial time, they have remained theoretical and have not been implemented in practical contexts to our knowledge. Here we use one of those algorithms to investigat...

متن کامل

The active bijection in graphs, hyperplane arrangements, and oriented matroids, 1: The fully optimal basis of a bounded region

The present paper is the first in a series of four dealing with a mapping, introduced by the present authors, from orientations to spanning trees, from regions to simplices in real hyperplane arrangements, from reorientations to bases in oriented matroids (in order of increasing generality). This mapping is actually defined for oriented matroids on a linearly ordered ground set. We call it the ...

متن کامل

Investigating the Effects of Contractual Factors and Arrangements on the Optimum Level of Production in Oil and Gas Projects: Evidence from the South Pars Phases 17 & 18

D evelopment of oil and gas fields is facing many risks, which are mainly due to uncertainties about the existence of commercial reserves, natural and economic environment, political conditions of host countries, legal and infrastructure issues and a market for petroleum products. In such an environment, investors are often engaged as contractors to develop and operate petroleum proj...

متن کامل

A Linear Programming Construction of Fully Optimal Bases in Graphs and Hyperplane Arrangements

The fully optimal basis of a bounded acyclic oriented matroid on a linearly ordered set has been defined and studied by the present authors in a series of papers, dealing with graphs, hyperplane arrangements, and oriented matroids (in order of increasing generality). This notion provides a bijection between bipolar orientations and uniactive internal spanning trees in a graph resp. bounded regi...

متن کامل

On the Arrangement Complexity of Uniform Trees

This paper studies the arrangement problem of uniform trees and shows that the arrangement complexity of a uniform tree is either (1) or ((lg n))(> 0). It also presents a recursive algorithm to compute the optimal complete arrangements for (1) arrangeable balanced uniform trees.

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1983