In the derivation of the spectral graph partitioning algorithm, we relax a combinatorial optimization problem to a continuous optimization problem. This relaxation has the following effects. The combinatorial problem requires an ex- act bisection of the graph, but the continuous al- gorithm can produce (after rounding) partitions that aren't perfectly balanced The combinatorial problem cannot be modi- fied to accommodate vertices that have different masses, whereas the continuous problem can The combinatorial problem requires finding eigenvectors, whereas the continuous problem re- quires only matrix multiplication ■The combinatorial problem is NP-hard, but the continuous problem can be solved in polyno- mial time

In the derivation of the spectral graph partitioning algorithm, we relax a combinatorial optimization problem to a continuous optimization problem. This relaxation has the following effects. The combinatorial problem requires an ex- act bisection of the graph, but the continuous al- gorithm can produce (after rounding) partitions that aren't perfectly balanced The combinatorial problem cannot be modi- fied to accommodate vertices that have different masses, whereas the continuous problem can The combinatorial problem requires finding eigenvectors, whereas the continuous problem re- quires only matrix multiplication ■The combinatorial problem is NP-hard, but the continuous problem can be solved in polyno- mial time

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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