Search Results

We show that if the nearly linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly solve all systems of linear equations over the reals. ...

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a 1-ε approximation to the multicommodity flow problem on graphs is a well-studied problem. In this paper we ...

We combine the work of Garg and Konemann, and Fleischer with ideas from dynamic graph algorithms to obtain faster (1-ε)-approximation schemes for various versions of the multicommodity flow problem. In particular, if ε is moderately small and the size ...

A preprocessing technique, Guided Design Search (GDS), is presented for the fixed-charge multicommodity capacitated network design (FCMD) problem. GDS applies design of experiment (DOE) principles in order to identify the critical edges in FCMD by ...

We present cycle-based algorithmic approaches to find local minima of a nonconvex and nonsmooth model for capacity expansion of a network supporting multicommodity flows. By exploiting complete optimality conditions for local minima, we give the ...

<P>This article describes the authors' experience solving large multicommodity flow problems with an embedded network simplex algorithm augmented with a fast-start heuristic for choosing an initial basis. The heuristic makes successive capacity ...

Fast algorithms that find approximate solutions for a general class of problems, which are called fractional packing and covering problems, are presented. The only previously known algorithms for solving these problems are based on general linear ...

A multicommodity flow problem is considered where for each pair of vertices (u, v) it is required to send f half-units of commodity (u, v) from u to v and f half-units of commodity (v, u) from v to u without violating capacity constraints. The main ...

This paper is concerned with the problem min $\{ f(x)\mid x \in X\} $ where X is a convex subset of a linear space H, and f is a smooth real-valued function on H. We propose the class of methods $x_{k + 1} = P(x_k - \alpha _k g_k )$, where P denotes ...