Approximate Shifted Combinatorial Optimization

TL;DR

This paper introduces the shifted combinatorial optimization framework, extending standard problems to a more complex nonlinear setting, and explores approximation algorithms for solving these challenging problems.

Contribution

It initiates the study of approximation algorithms specifically designed for the new shifted combinatorial optimization framework.

Findings

Framework captures diverse combinatorial problems

Shifted problems are generally harder than standard ones

Provides initial approximation strategies for the new class

Abstract

Shifted combinatorial optimization is a new nonlinear optimization framework, which is a broad extension of standard combinatorial optimization, involving the choice of several feasible solutions at a time. It captures well studied and diverse problems ranging from congestive to partitioning problems. In particular, every standard combinatorial optimization problem has its shifted counterpart, which is typically much harder. Here we initiate a study of approximation algorithms for this broad optimization framework.