Multicommodity Flow

نویسندگان

  • Dana Randall
  • Sang-Ho Shim
چکیده

Leighton and Rao use multicommodity flow results to design the first polynomial time approximation algorithms for well known NP-Hard optimization problems. Such problems include graph partitioning, crossing number, VLSI layout, and many more. Furthermore, Leighton and Rao are responsible for establishing the max-flow min-cut theorems on multicommodity flow problems, which lead to the algorithms mentioned above. In this paper we will establish the definitions and lemmas necessary to understand multicommodity flow problems, and we will also present the influential max-flow min-cut theorem by Leighton and Rao.

برای دانلود 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

Uncertain minimum cost multicommodity flow problem

This paper investigates the minimum cost multicommodity flow problem with uncertain costs and uncertain capacities. Uncertainty theory is used to deal with indeterminacy factors in uncertain network. An (α, β)-minimum cost multicommodity flow model is formulated. Some properties of the model are analyzed. An equivalence relationship between the (α, β)-minimum cost multicommodity flow and the mi...

متن کامل

Optimal multicommodity flows in dynamic networks and algorithms for their finding

In this paper we study two basic problems related to dynamic flows: maximum multicommodity flow and the minimum cost multicommodity flow problems. We consider these problems on dynamic networks with time-varying capacities of edges. For minimum cost multicommodity flow problem we assume that cost functions, defined on edges, are nonlinear and depending on time and flow, and the demand function ...

متن کامل

Advances in Solving the Multicommodity-Flow Problem

The multicommodity-flow problem arises in a wide variety of important applications. Many communications, logistics, manufacturing , and transportation problems can be formulated as large multicommodity-flow problems. During the last few years researchers have made steady advances in solving extremely large multicommodity-flow problems. This improvement has been due both to algorithmic and to ha...

متن کامل

M ay 2 01 2 Faster Approximate Multicommodity Flow Using Quadratically Coupled Flows ∗

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1 − ǫ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical p...

متن کامل

Faster approximate multicommodity flow using quadratically coupled flows Citation

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1 − ǫ approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we present an adaptation of recent advances in single-commodity flow algorithms to this problem. As the underlying linear systems in the electrical p...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005