Paper by Erik D. Demaine

Reference:

Noga Alon, Erik D. Demaine, MohammadTaghi Hajiaghayi, and Tom Leighton, “Basic Network Creation Games”, in Proceedings of the 22nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA 2010), Santorini, Greece, June 13–15, 2010, pages 21–29.

Abstract:

We study a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes, by swapping one incident edge at a time. The central question is what structure the resulting equilibrium graphs have, in particular, how well they globally minimize diameter. For the local-average-distance version, we prove an upper bound of 2^O(√lg n), a lower bound of 3, a tight bound of exactly 2 for trees, and give evidence of a general polylogarithmic upper bound. For the local-diameter version, we prove a lower bound of Ω(√n), and a tight upper bound of 3 for trees. All of our upper bounds apply equally well to previously extensively studied network creation games, both in terms of the diameter metric described above and the previously studied price of anarchy (which are related by constant factors). In surprising contrast, our model has no parameter α for the link creation cost, so our results automatically apply for all values of α without additional effort; furthermore, equilibrium can be checked in polynomial time in our model, unlike previous models. Our perspective enables simpler and more general proofs that get at the heart of network creation games.

Comments:

This paper is also available from the ACM Digital Library.

Updates:

Unfortunately the proof of Theorem 5 is flawed, but the theorem is still true. Read our erratum for a correct proof.

Length:

The paper is 8 pages.

Availability:

The paper is available in PostScript (388k), gzipped PostScript (155k), and PDF (263k).

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