A \(o(n)\)-Competitive Deterministic Algorithm for Online Matching on a Line
Online matching on a line involves matching an online stream of items of various sizes to stored items of various sizes, with the objective of minimizing the average discrepancy in size between matched items. The best previously known upper and lower bounds on the optimal deterministic competitive ratio are linear in the number of items, and constant, respectively. We show that online matching on a line is essentially equivalent to a particular search problem, that we call \(k\) -lost cows. We then obtain the first deterministic sub-linearly competitive algorithm for online matching on a line by giving such an algorithm for the \(k\)-lost cows problem.
KeywordsCompetitive Ratio Online Algorithm Search Problem Deterministic Algorithm Optimal Match
- 8.Kalyanasundaram, B., Pruhs, K.: Online network optimization problems. Online Algorithms 1996. LNCS, vol. 1442, pp. 268–280. Springer, Heidelberg (1998)Google Scholar
- 14.López-Ortiz., A.: On-line target searching in bounded and unbounded domains. Ph.D thesis, University of Waterloo (1996)Google Scholar
- 15.Meyerson, A., Nanavati, A., Poplawski, L.J.: Randomized online algorithms for minimum metric bipartite matching. In: Proceedings of the 17th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 954–959 (2006)Google Scholar