Online computation and competitive analysis
Online computation and competitive analysis
Developments from a June 1996 seminar on Online algorithms: the state of the art
Developments from a June 1996 seminar on Online algorithms: the state of the art
Optimal On-Line Algorithms for Single-Machine Scheduling
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Online Dial-a-Ride Problems: Minimizing the Completion Time
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
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In the online traveling salesman problem requests for visits to cities (points in a metric space) arrive online while the salesman is traveling. The salesman moves at no more than unit speed and starts and ends his work at a designated origin. The objective is to find a routing for the salesman which finishes as early as possible. We consider the online traveling salesman problem when restricted to the non-negative part of the real line. We show that a very natural strategy is 3/2-competitive which matches our lower bound. The main contribution of the paper is the presentation of a "fair adversary", as an alternative to the omnipotent adversary used in competitive analysis for online routing problems. The fair adversary is required to remain inside the convex hull of the requests released so far. We show that on IR0+ algorithms can achieve a strictly better competitive ratio against a fair adversary than against a conventional adversary. Specifically, we present an algorithm against a fair adversary with competitive ratio (1+√17)/4 ≅ 1:28 and provide a matching lower bound. We also show competitiveness results for a special class of algorithms (called diligent algorithms) that do not allow waiting time for the server as long as there are requests unserved.