sigact28revised.pdf (771.13 kB)
Download file

SIGACT News Online Algorithms Column 28: Online Matching on the Line, Part 2

Download (771.13 kB)
journal contribution
posted on 21.11.2016, 16:27 by Rob Van Stee
In the online matching problem on the line, requests (points in R) arrive one by one to be served by a given set of servers. Each server can be used only once. This is a variant of the k-server problem restricted to the real line. Although easy to state, this problem is stil wide open. The best known lower bound is 9.001 [2], showing that this problem is really different from the well-known cow path problem. Antoniadis et al. [1] recently presented a sublinearly competitive algorithm. In this column, I present some results by Elias Koutsoupias and Akash Nanavati on this problem with kind permission of the authors. The column is based on Akash’ PhD thesis [4], which contains an extended version of their joint WAOA 2003 paper [3] which has never appeared in a journal. I have expanded the proofs and slightly reorganized the presentation. The previous column (see SIGACT News 47(1):99-111) contains a proof of a linear upper bound for the generalized work function algorithm and a logarithmic lower bound for the algorithm. This column gives a more detailed analysis of this algorithm, leading to a different (but again linear) upper bound. The techniques used here may potentially be helpful to show a sublinear upper bound for γ-wfa. I conjecture that this algorithm in fact has a logarithmic competitive ratio (which would match the known lower bound for it), but this very much remains an open question.



SIGACT News, 2016, 47 (2), pp. 40-51

Author affiliation

/Organisation/COLLEGE OF SCIENCE AND ENGINEERING/Department of Computer Science


AM (Accepted Manuscript)

Published in



Association for Computing Machinery

Copyright date


Available date


Publisher version


The final published version is available through the links above.



Usage metrics