Distributed Transactional Contention Management as the Traveling Salesman Problem

Abstract

In this paper we consider designing contention managers for distributed software transactional memory (DTM), given an input of n transactions sharing s objects in a network of m nodes. We first construct a dynamic ordering conflict graph $G_c^{*}(\phi(\kappa))$ for an offline algorithm (κ,φ _κ ). We show that finding an optimal schedule is equivalent to finding the offline algorithm for which the weight of the longest weighted path in $G_c^{*}(\phi(\kappa))$ is minimized. We further illustrate that when the set of transactions are dynamically generated, processing transactions according to a χ(G _c )-coloring of G _c does not lead to an optimal schedule, where χ(G _c ) is the chromatic number of G _c . We prove that, for DTM, any online work conserving deterministic contention manager provides an $\Omega(\max[s,\frac{s^2}{\overline{D}}])$ competitive ratio in a network with normalized diameter $\overline{D}$. Compared with the Ω(s) competitive ratio for multiprocessor STM, the performance guarantee for DTM degrades by a factor proportional to $\frac{s}{\overline{D}}$. To break this lower bound, we present a randomized algorithm Cutting, which needs partial information of transactions and an approximate algorithm A for the traveling salesman problem with approximation ratio φ _A . We show that the average case competitive ratio of Cutting is $O\big(s\cdot \phi_A\cdot\log^{2} m\log^{2} n\big)$, which is close to O(s).