Ordering heuristics for parallel graph coloring

Hasenplaugh, William; Kaler, Tim; Schardl, Tao B.; Leiserson, Charles E.

doi:10.1145/2612669.2612697

Cited by 85 publications

(61 citation statements)

References 48 publications

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“…William Hasenplaugh and Chia-Hsin Chen graciously shared the serial code for the color [30] and nocsim benchmarks. This work was supported in part by C-FAR, one of six SRC STARnet centers by MARCO and DARPA, and by NSF grants CAREER-1452994 and CCF-1318384.…”

Section: Acknowledgmentsmentioning

confidence: 99%

Data-centric execution of speculative parallel programs

Jeffrey

Subramanian

Abeydeera

et al. 2016

2016 49th Annual IEEE/ACM International Symposium on Microarchitecture (MICRO)

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Abstract-Multicore systems must exploit locality to scale, scheduling tasks to minimize data movement. While localityaware parallelism is well studied in non-speculative systems, it has received little attention in speculative systems (e.g., HTM or TLS), which hinders their scalability.We present spatial hints, a technique that leverages program knowledge to reveal and exploit locality in speculative parallel programs. A hint is an abstract integer, given when a speculative task is created, that denotes the data that the task is likely to access. We show it is easy to modify programs to convey locality through hints. We design simple hardware techniques that allow a state-of-the-art, tiled speculative architecture to exploit hints by: (i) running tasks likely to access the same data on the same tile, (ii) serializing tasks likely to conflict, and (iii) balancing tasks across tiles in a locality-aware fashion. We also show that programs can often be restructured to make hints more effective.Together, these techniques make speculative parallelism practical on large-scale systems: at 256 cores, hints achieve nearlinear scalability on nine challenging applications, improving performance over hint-oblivious scheduling by 3.3× gmean and by up to 16×. Hints also make speculation far more efficient, reducing wasted work by 6.4× and traffic by 3.5× on average.

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Section: Acknowledgmentsmentioning

confidence: 99%

Data-centric execution of speculative parallel programs

Jeffrey

Subramanian

Abeydeera

et al. 2016

2016 49th Annual IEEE/ACM International Symposium on Microarchitecture (MICRO)

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“…csail.mit.edu. To implement the GET-COLOR procedure, the PRISM implementation used a deterministic multicore coloring algorithm [52], which was also coded in Cilk Plus. For comparison, we engineered three other schedulers for executing dynamic datagraph computations in parallel:…”

Section: Methodsmentioning

confidence: 99%

“…Although it is NP-complete to find either an optimal coloring of a graph [40] -a coloring that uses the smallest possible number of colors -or a O(V ε )-approximation of the optimal col- oring [77], as Section 6 discusses, an optimal coloring is not necessary for PRISM to perform well in practice, as long as the data graph is colored with sufficiently few colors. Many parallel coloring algorithms exist that satisfy the needs of PRISM (see, for example, [3,5,45,46,52,59,61,62,73,94]). In fact, if the data-graph computation performs sufficiently many updates, a Θ(V + E)-work greedy coloring algorithm, such as that introduced by Welsh and Powell [96], can suffice as well.…”

Section: The Prism Algorithmmentioning

confidence: 99%

“…In fact, if the data-graph computation performs sufficiently many updates, a Θ(V + E)-work greedy coloring algorithm, such as that introduced by Welsh and Powell [96], can suffice as well. Our program implementation of PRISM uses a multicore variant of the Jones and Plassmann algorithm [59] that produces a deterministic (∆ + 1)-coloring of a degree-∆ graph G = (V, E) in linear work and O(lgV + lg ∆ · min{ √ E, ∆ + lg ∆ lgV / lg lgV }) span [52]. Let us now see how PRISM uses chromatic scheduling to execute a dynamic data-graph computation G, f , Q 0 .…”

Section: The Prism Algorithmmentioning

confidence: 99%

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Executing Dynamic Data-Graph Computations Deterministically Using Chromatic Scheduling

Kaler

Hasenplaugh

Schardl

et al. 2016

ACM Trans. Parallel Comput.

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A data-graph computation -popularized by such programming systems as Galois, Pregel, GraphLab, PowerGraph, and GraphChi -is an algorithm that performs local updates on the vertices of a graph. During each round of a data-graph computation, an update function atomically modifies the data associated with a vertex as a function of the vertex's prior data and that of adjacent vertices. A dynamic data-graph computation updates only an active subset of the vertices during a round, and those updates determine the set of active vertices for the next round.This paper introduces PRISM, a chromatic-scheduling algorithm for executing dynamic data-graph computations. PRISM uses a vertex-coloring of the graph to coordinate updates performed in a round, precluding the need for mutual-exclusion locks or other nondeterministic data synchronization. A multibag data structure is used by PRISM to maintain a dynamic set of active vertices as an unordered set partitioned by color. We analyze PRISM using work-span analysis. Let G = (V, E) be a degree-∆ graph colored with χ colors, and suppose that Q ⊆ V is the set of active vertices in a round. Define size(Q) = |Q| + v∈Q deg(v), which is proportional to the space required to store the vertices of Q using a sparsegraph layout. We show that a P-processor execution of PRISM performs updates in Q using O(χ(lg(Q/χ) + lg ∆) + lg P) span and Θ(size(Q) + χ + P) work. These theoretical guarantees are matched by good empirical performance. We modified GraphLab to incorporate PRISM and studied seven application benchmarks on a 12-core multicore machine. PRISM executes the benchmarks 1.2-2.1 times faster than GraphLab's nondeterministic lock-based scheduler while providing deterministic behavior. This paper also presents PRISM-R, a variation of PRISM that executes dynamic data-graph computations deterministically even when updates modify global variables with associative operations. PRISM-R satisfies the same theoretical bounds as PRISM, but its implementation is more involved, incorporating a multivector data structure to maintain an ordered set of vertices partitioned by color.

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“…al. provide a comprehensive overview of sequential an parallel graph colouring algorithms using a number of different node ordering heuristics [6]. In many applications, an optimal colouring is considered to be one in which the total number of colours is minimised.…”

Section: Colouring Algorithmsmentioning

confidence: 99%

Analysis of the semi-synchronous approach to large-scale parallel community finding

Duriakova

Hurley

Ajwani³

et al. 2014

Proceedings of the Second ACM Conference on Online Social Networks

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Community-finding in graphs is the process of identifying highly cohesive vertex subsets. Recently the vertex-centric approach has been found effective for scalable graph processing and is implemented in systems such as GraphLab and Pregel. In the vertex-centric approach, the analysis is decomposed into a set of local computations at each vertex of the graph, with results propagated to neighbours along the vertex's edges. Many community finding algorithms are amenable to this approach as they are based on the optimisation of an objective through a process of iterative local update (ILU), in which vertices are successively moved to the community of one of their neighbours in order to achieve the highest local gain in the quality of the objective. The sequential processing of such iterative algorithms generally benefits from an asynchronous approach, where a vertex update uses the most recent state as generated by the previous update of vertices in its neighbourhood. When vertices are distributed over a parallel machine, the asynchronous approach can encounter race conditions that impact on its performance and destroy the consistency of the results. Alternatively, a semi-synchronous approach ensures that only non-conflicting vertices are updated simultaneously. In this paper we study the semi-synchronous approach to ILU algorithms for community finding on social networks. Because of the heavy-tailed vertex distribution, the order in which vertex updates are applied in asynchronous ILU can greatly impact both convergence time and quality of the found communities. We study the impact of ordering on the distributed label propagation and modularity maximisation algorithms implemented on a shared-memory multicore architecture. We demonstrate that the semi-synchronous ILU approach is competitive in time and quality with the asynchronous approach, while allowing the analyst to maintain consistent control over update ordering. Thus, our implementation results in a more robust and predictable performance and provides control over the order in which the node Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. labels are updated, which is crucial to obtaining the correct trade-off between running time and quality of communities on many graph classes.

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Ordering heuristics for parallel graph coloring

Cited by 85 publications

References 48 publications

Data-centric execution of speculative parallel programs

Data-centric execution of speculative parallel programs

Executing Dynamic Data-Graph Computations Deterministically Using Chromatic Scheduling

Analysis of the semi-synchronous approach to large-scale parallel community finding

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