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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Multithreaded Algorithms for Graph Coloring

Graph algorithms are challenging to parallelize when high performance and scalability are primary goals. Low concurrency, poor data locality, irregular access pattern, and high data access to computation ratio are among the chief reasons for the challenge. The performance implication of these features is exasperated on distributed memory machines. More success is being achieved on shared-memory, multi-core architectures supporting multithreading. We consider a prototypical graph problem, coloring, and show how a greedy algorithm for solving it can be e*ectively parallelized on multithreaded architectures. We present in particular two di*erent parallel algorithms. The first relies on speculation and iteration, and is suitable for any shared-memory, multithreaded system. The second uses data ow principles and is targeted at the massively multithreaded Cray XMT system. We benchmark the algorithms on three di*erent platforms and demonstrate scalable runtime performance. In terms of quality of solution, both algorithms use nearly the same number of colors as the serial algorithm.

Catalyurek, Umit V↗
DOE OSTI2017

Algorithms for Balanced Graph Colorings with Applications in Parallel Computing

Graph coloring is used to identify subsets of independent tasks in parallel scientific computing applications. Traditional coloring heuristics aim to reduce the number of colors used as that number also corresponds to the number of parallel steps in the application. However, if the color classes produced have a skew in their sizes, utilization of hardware resources becomes inefficient, especially for the smaller color classes. Equitable coloring is a theoretical formulation of coloring that guarantees a perfect balance among color classes, and its practical relaxation is referred to as balanced coloring. In this paper, we revisit the problem of balanced coloring in the context of parallel computing. The goal is to achieve a balanced coloring of an input graph without increasing the number of colors that an algorithm oblivious to balance would have used. We propose and study multiple heuristics that aim to achieve such a balanced coloring for two variants of coloring problem, distance-1 coloring and partial distance-2 coloring (defined on a bipartite graph). We present parallelization approaches for multi-core and manycore architectures, and cross-evaluate their effectiveness with respect to the quality of balance achieved and performance. Furthermore, we study the impact of the proposed balanced coloring heuristics on a concrete application - viz. parallel community detection, which is an example of an irregular application. In addition, we propose several extensions to our balancing schemes and evaluate their balancing efficacy and performance characteristics. The thorough treatment of balanced coloring presented in this paper from algorithms to application is expected to serve as a valuable resource to parallel application developers who seek to improve parallel performance of their applications using coloring.

graph coloring, multithreaded algorithms↗
DOE OSTI2024

Picasso: Memory-Efficient Graph Coloring Using Palettes With Applications in Quantum Computing

A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and a parallel implementation of the proposed algorithm. We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

artificial intelligence, quantum computing↗
DOE OSTI2022

Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Experience of Migrating a Parallel Graph Coloring Program from CUDA to SYCL

We describe the experience of converting a CUDA implementation of a parallel graph coloring algorithm to SYCL. The goals are for our work to be useful to application and compiler developers by providing a detailed description of migration paths between CUDA and SYCL. We will describe how CUDA functions are mapped to SYCL functions. Evaluating the CUDA and SYCL implementations of the algorithm shows that the performance of SYCL and CUDA kernels are comparable over the test graph set on NVIDIA P100 and V100 GPUs. The SYCL program also allows for performance evaluation with the OpenCL and Level Zero interfaces and power profiling on an Intel GPU computing platform.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Planning for Compilation of a Quantum Algorithm for Graph Coloring

Recently, the problem of compiling general quantum algorithms for implementation on near-term quantum processors has been introduced to the AI community. Previous work demonstrated that temporal planning is an attractive approach for part of this compilation task, specifically, the routing of circuits that implement the Quantum Alternating Operator Ansatz (QAOA) applied to theMaxCut problem on a quantum processor architecture. In this paper, we extend the earlier work to route circuits that implement QAOAfor Graph Coloring problems. QAOA for coloring requires execution of more, and more complex, operations on the chip, which makes routing a more challenging problem. We evaluate the approach on state-of-the-art hardware architectures from leading quantum computing companies. Additionally, we investigate applying the planning approach to qubit initialization as well as routing. Our empirical evaluation shows that temporal planning compares well to reasonable analytic upper bounds [20], and that solving qubit initialization with a classical planner generally helps temporal planners in finding shorter-makespan compilations for QAOA for Graph Coloring.These advances suggest that temporal planning can be an effective approach for more complex quantum computing algorithms and architectures.

Minh Do↗
NASA NTRS2019

Using Graph Coloring to Compute Total Derivatives More Efficiently in OpenMDAO

When they are applicable, gradient based optimization algorithms are the most efficient way to solve design optimization problems. Although gradient based methods are generally efficient, they can be made significantly more so through the usage of analytic techniques to compute the necessary total derivatives. The traditional forward (direct) and reverse (adjoint) analytic techniques have computational costs that scale linearly with the number of design variables and the number of constraints, respectively. In this work, we present an application of a graph coloring algorithm to the analytic techniques for computing total derivative Jacobians in order to achieve much better computational scaling than the pure analytic methods can provide alone. A detailed theoretical explanation of how coloring algorithms interact with analytic derivative methods is presented that illustrates specific types of sparsity patterns that must be present in total derivative Jacobians in order for this coloring technique to be effective. The new technique has been implemented as a feature in the OpenMDAO framework and the implementation is demonstrated on two example problems. The performance on the example problems up to 50% reduction in compute cost for optimizations with bi-directional coloring compared to traditional constraint aggregation. Additionally, the results show how coloring technique alleviates some of the numerical difficulties that constraint aggregation can cause, leading to the ability to solve larger problems. It is expected that the new method will have wide applicability to multidisciplinary optimization problems, and that its availability in OpenMDAO will offer significant computational savings for users without the need for them to implement the coloring algorithm themselves.

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