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Theoretical Approaches to Node Assignment David G. Andersen

Summary: Theoretical Approaches to Node Assignment
David G. Andersen
December 23, 2002
1 Abstract
In this paper, we provide a survey and explanation of several methods for approximating the NP-hard
problem of nding a multiway separator in a graph. This is motivated by the problem of assigning
nodes in an ethernet switch connected testbed without violating bandwidth constraints. As a critical
component of the multiway separator problem, we discuss in some detail the sparse cut problem, with
several modern O(log k) approaches, which result in realizable O(log 2 k) approximations to the multiway
separator problem, and some even better theoretical bounds. Finally, we conclude with a less formal
discussion of the mapping of the more general typed-nodes testbed problem to the multiway separator
2 Introduction
The Flux Testbed project at the University of Utah is designing a network emulation testbed, consisting
of PCs with multiple ethernet interfaces connected to switches. The switches have (e ectively) in nite
internal bandwidth. These switches are then connected to a master switch with links of nite bandwidth.
A user of the testbed provides a description of the desired logical network they wish to emulate. One
problem that has arisen is the assignment of physical nodes to logical nodes. An incorrect assignment
could result in too much tra∆c going between switches, resulting in unintended interference between
supposedly unrelated links in the user's experiment. In the most general case, there may be multiple


Source: Andersen, Dave - School of Computer Science, Carnegie Mellon University


Collections: Computer Technologies and Information Sciences