A Fast and Scalable Graph Coloring Algorithm for Multi-core and Many-core Architectures

Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The total run time of a coloring algorithm adds to the overall parallel overhead of the application whereas the number of colors used determines the amount of exposed parallelism. A fast and scalable coloring algorithm using as few colors as possible is vital for the overall parallel performance and scalability of many irregular applications that depend upon runtime dependency analysis. Catalyurek et al. have proposed a graph coloring algorithm which relies on speculative, local assignment of colors. In this paper we present an improved version which runs even more optimistically with less thread synchronization and reduced number of conflicts compared to Catalyurek et al.'s algorithm. We show that the new technique scales better on multi-core and many-core systems and performs up to 1.5x faster than its predecessor on graphs with high-degree vertices, while keeping the number of colors at the same near-optimal levels.Comment: To appear in the proceedings of Euro Par 201

Exploiting Multiple Levels of Parallelism in Sparse Matrix-Matrix Multiplication

Sparse matrix-matrix multiplication (or SpGEMM) is a key primitive for many high-performance graph algorithms as well as for some linear solvers, such as algebraic multigrid. The scaling of existing parallel implementations of SpGEMM is heavily bound by communication. Even though 3D (or 2.5D) algorithms have been proposed and theoretically analyzed in the flat MPI model on Erdos-Renyi matrices, those algorithms had not been implemented in practice and their complexities had not been analyzed for the general case. In this work, we present the first ever implementation of the 3D SpGEMM formulation that also exploits multiple (intra-node and inter-node) levels of parallelism, achieving significant speedups over the state-of-the-art publicly available codes at all levels of concurrencies. We extensively evaluate our implementation and identify bottlenecks that should be subject to further research

Optimal Collision/Conflict-free Distance-2 Coloring in Synchronous Broadcast/Receive Tree Networks

This article is on message-passing systems where communication is (a) synchronous and (b) based on the "broadcast/receive" pair of communication operations. "Synchronous" means that time is discrete and appears as a sequence of time slots (or rounds) such that each message is received in the very same round in which it is sent. "Broadcast/receive" means that during a round a process can either broadcast a message to its neighbors or receive a message from one of them. In such a communication model, no two neighbors of the same process, nor a process and any of its neighbors, must be allowed to broadcast during the same time slot (thereby preventing message collisions in the first case, and message conflicts in the second case). From a graph theory point of view, the allocation of slots to processes is know as the distance-2 coloring problem: a color must be associated with each process (defining the time slots in which it will be allowed to broadcast) in such a way that any two processes at distance at most 2 obtain different colors, while the total number of colors is "as small as possible". The paper presents a parallel message-passing distance-2 coloring algorithm suited to trees, whose roots are dynamically defined. This algorithm, which is itself collision-free and conflict-free, uses $\Delta + 1$ colors where $\Delta$ is the maximal degree of the graph (hence the algorithm is color-optimal). It does not require all processes to have different initial identities, and its time complexity is $O(d \Delta)$, where d is the depth of the tree. As far as we know, this is the first distributed distance-2 coloring algorithm designed for the broadcast/receive round-based communication model, which owns all the previous properties.Comment: 19 pages including one appendix. One Figur