A Competitive Analysis for Balanced Transactional Memory Workloads

TL;DR

This paper analyzes the theoretical limits of contention management algorithms for balanced transactional memory workloads, introducing two new algorithms with improved competitive ratios and proving their optimality under certain complexity assumptions.

Contribution

It presents two new greedy contention management algorithms with competitive ratios of O(√s) and O(√s log n), improving upon prior bounds and establishing their tightness.

Findings

Clairvoyant algorithm is O(√s)-competitive, depending on the conflict graph.

Non-Clairvoyant algorithm is O(√s log n)-competitive, without needing conflict graph knowledge.

The performance bounds are proven to be tight unless NP is in ZPP.

Abstract

We consider transactional memory contention management in the context of balanced workloads, where if a transaction is writing, the number of write operations it performs is a constant fraction of its total reads and writes. We explore the theoretical performance boundaries of contention management in balanced workloads from the worst-case perspective by presenting and analyzing two new contention management algorithms. The first algorithm Clairvoyant is O(\surd s)-competitive, where s is the number of shared resources. This algorithm depends on explicitly knowing the conflict graph. The second algorithm Non-Clairvoyant is O(\surd s \cdot log n)-competitive, with high probability, which is only a O(log n) factor worse, but does not require knowledge of the conflict graph, where n is the number of transactions. Both of these algorithms are greedy. We also prove that the performance of Clairvoyant is tight since there is no contention management algorithm that is better than O((\surd s)^(1-\epsilon))-competitive for any constant \epsilon > 0, unless NP\subseteq ZPP. To our knowledge, these results are significant improvements over the best previously known O(s) competitive ratio bound.