The distributed (Δ + 1)-coloring problem is one of most fundamental and well-studied problems in Distributed Algorithms. Starting with the work of Cole and Vishkin in 86, there was a long line of gradually improving algorithms published. The current state-of-the-art running time is O(Δ log Δ + log* n), due to Kuhn and Wattenhofer, PODC'06. Linial (FOCS'87) has proved a lower bound of 1/2 log* n for the problem, and Szegedy and Vishwanathan (STOC'93) provided a heuristic argument that shows that algorithms from a wide family of locally iterative algorithms are unlikely to achieve running time smaller than Θ(Δ log Δ). We present a deterministic (Δ + 1)-coloring distributed algorithm with running time O(Δ) + 1/2 log* n. We also present a tradeoff between the running time and the number of colors, and devise an O(Δ • t)-coloring algorithm with running time O(Δ / t + log* n), for any parameter t, 1

/pdf/distributed-d-1-coloring-in-linear-in-d-time-2e80k0idhu.pdf

Distributed (δ+1)-coloring in linear (in δ) time

The distributed $(\Delta + 1)$-coloring problem is one of the most fundamental and well-studied problems in distributed algorithms Starting with the work of Cole and Vishkin in 1986, a long line of gradually improving algorithms has been published The state-of-the-art running time, prior to our work, is $O(\Delta \log \Delta + \log^* n)$, due to Kuhn and Wattenhofer [Proceedings of the $25$th Annual ACM Symposium on Principles of Distributed Computing, Denver, CO, 2006, pp 7--15] Linial [Proceedings of the $28$th Annual IEEE Symposium on Foundation of Computer Science, Los Angeles, CA, 1987, pp 331--335] proved a lower bound of $\frac{1}{2} \log^* n$ for the problem, and Szegedy and Vishwanathan [Proceedings of the 25th Annual ACM Symposium on Theory of Computing, San Diego, CA, 1993, pp 201--207] provided a heuristic argument that shows that algorithms from a wide family of locally iterative algorithms are unlikely to achieve a running time smaller than $\Theta(\Delta \log \Delta)$ We present a de

Distributed $(\Delta+1)$-Coloring in Linear (in $\Delta$) Time

With nearest-neighbor load-balancing algorithms, a processor makes balancing decisions based on localized workload information and manages workload migrations within its neighborhood. The paper compares a couple of fairly well-known nearest-neighbor algorithms, the dimension-exchange (DE) and the diffusion (DF) methods and their several variants—the average dimension-exchange (ADE), optimally tuned dimension-exchange (ODE), local average diffusion (ADF) and optimally tuned diffusion (ODF). The measures of interest are their efficiency in driving any initial workload distribution to a uniform distribution and their ability in controlling the growth of the variance among the processors' workloads. The comparison is made with respect to both one-port and all-port communication architectures and in consideration of various implementation strategies including synchronous/asynchronous invocation policies and static/dynamic random workload behaviors. It turns out that the dimension-exchange method outperforms the diffusion method in the one-port communication model. In particular, the ODE algorithm is best suited for statically synchronous implementations of a load-balancing process regardless of its underlying communication models. The strength of the diffusion method is in asynchronous implementations in the all-port communication model; the ODF algorithm performs best in that case. The underlying communication networks considered assume the most popular topologies, the mesh and the torus and their special cases: the hypercube and the k-ary n-cube.

Nearest-neighbor algorithms for load-balancing in parallel computers

Analysis of the generalized dimension exchange method for dynamic load balancing

Parallel scheduling is a new approach for load balancing. In parallel scheduling, all processors cooperate to schedule work. Parallel scheduling is able to accurately balance the load by using global load information at compile-time or runtime. It provides high-quality load balancing. This paper presents an overview of the parallel scheduling technique. Scheduling algorithms for tree, hypercube, and mesh networks are presented. These algorithms can fully balance the load and maximize locality at runtime. Communication costs are significantly reduced compared to other existing algorithms.

On runtime parallel scheduling for processor load balancing

Analysis of a graph coloring based distributed load balancing algorithm

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Analysis of a graph coloring based distributed load balancing algorithm