Online Mixed Packing and Covering
Umang Bhaskar, Lisa Fleischer

TL;DR
This paper introduces the first polylogarithmic-competitive online algorithms for mixed packing and covering linear programs, addressing the challenge of online constraints with applications to machine scheduling and facility location.
Contribution
It presents the first sublinear competitive algorithms for online mixed packing and covering linear programs, using exponential penalty functions and multiplicative updates.
Findings
First polylogarithmic-competitive algorithm for mixed packing and covering LPs
Nearly tight lower bound established for the problem
Extended techniques to online fixed-charge problems with congestion
Abstract
In many problems, the inputs arrive over time, and must be dealt with irrevocably when they arrive. Such problems are online problems. A common method of solving online problems is to first solve the corresponding linear program, and then round the fractional solution online to obtain an integral solution. We give algorithms for solving linear programs with mixed packing and covering constraints online. We first consider mixed packing and covering linear programs, where packing constraints are given offline and covering constraints are received online. The objective is to minimize the maximum multiplicative factor by which any packing constraint is violated, while satisfying the covering constraints. No prior sublinear competitive algorithms are known for this problem. We give the first such --- a polylogarithmic-competitive algorithm for solving mixed packing and covering linear…
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Taxonomy
TopicsOptimization and Search Problems · Vehicle Routing Optimization Methods · Complexity and Algorithms in Graphs
