Authors:
Christine Markarian
1
and
Friedhelm Meyer auf der Heide
2
Affiliations:
1
Department of Mathematical Sciences, Haigazian University, Beirut and Lebanon
;
2
Heinz Nixdorf Institute and Computer Science Department, University of Paderborn, Paderborn and Germany
Keyword(s):
Online Algorithms, Competitive Analysis, Leasing, Parking Permit Problem, Randomized Rounding, Primal-Dual Algorithms, Operations Research, Resource Allocation.
Related
Ontology
Subjects/Areas/Topics:
Applications
;
Artificial Intelligence
;
Game Theory
;
Information Systems
;
Knowledge Discovery and Information Retrieval
;
Knowledge-Based Systems
;
Methodologies and Technologies
;
Operational Research
;
Optimization
;
Pattern Recognition
;
Resource Allocation
;
Scheduling
;
Software Engineering
;
Symbolic Systems
Abstract:
We consider leasing variants of two classical N P-hard optimization problems, Vertex Cover (VC) and non-metric Facility Location (non-metric FL). These contain the well-known Parking Permit problem due to Meyerson [FOCS 2005] as a special sub-case and can be found as sub-problems in many operations research applications. We give the first online algorithms for these two problems, evaluated using the standard notion of competitive analysis in which the online algorithm whose input instance is revealed over time is compared to the optimal offline algorithm which knows the entire input sequence in advance and is optimal. Our algorithms have optimal and near-optimal competitive ratios for the leasing variants of VC and non-metric FL, respectively.