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Register a new userContention Resolution Without Collision Detection
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William Kuszmaul
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This paper focuses on the contention resolution problem on a shared communication channel that does not support collision detection. A shared communication channel is a multiple access channel, which consists of a sequence of synchronized time slots. Players on the channel may attempt to broadcast a packet (message) in any time slot. A players broadcast succeeds if no other player broadcasts during that slot. If two or more players broadcast in the same time slot, then the broadcasts collide and both broadcasts fail. The lack of collision detection means that a player monitoring the channel cannot differentiate between the case of two or more players broadcasting in the same slot (a collision) and zero players broadcasting. In the contention-resolution problem, players arrive on the channel over time, and each player has one packet to transmit. The goal is to coordinate the players so that each player is able to successfully transmit its packet within reasonable time. However, the players can only communicate via the shared channel by choosing to either broadcast or not. A contention-resolution protocol is measured in terms of its throughput (channel utilization). Previous work on contention resolution that achieved constant throughput assumed that either players could detect collisions, or the players arrival pattern is generated by a memoryless (non-adversarial) process. The foundational question answered by this paper is whether collision detection is a luxury or necessity when the objective is to achieve constant throughput. We show that even without collision detection, one can solve contention resolution, achieving constant throughput, with high probability.
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We give a 1.488-approximation for the classic scheduling problem of minimizing total weighted completion time on unrelated machines. This is a considerable improvement on the recent breakthrough of $(1.5 - 10^{-7})$-approximation (STOC 2016, Bansal-Srinivasan-Svensson) and the follow-up result of $(1.5 - 1/6000)$-approximation (FOCS 2017, Li). Bansal et al. introduced a novel rounding scheme yielding strong negative correlations for the first time and applied it to the scheduling problem to obtain their breakthrough, which resolved the open problem if one can beat out the long-standing $1.5$-approximation barrier based on independent rounding. Our key technical contribution is in achieving significantly stronger negative correlations via iterative fair contention resolution, which is of independent interest. Previously, Bansal et al. obtained strong negative correlations via a variant of pipage type rounding and Li used it as a black box.
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