We give efficient randomized and deterministic distributed algorithms for computing a distance-2 vertex coloring of a graph G in the CONGEST model. In particular, if Delta is the maximum degree of G, we show that ther...
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ISBN:
(纸本)9781450375825
We give efficient randomized and deterministic distributed algorithms for computing a distance-2 vertex coloring of a graph G in the CONGEST model. In particular, if Delta is the maximum degree of G, we show that there is a randomized CONGEST model algorithm to compute a distance-2 coloring of G with Delta(2) + 1 colors in O(log Delta . log n) rounds. Further if the number of colors is slightly increased to (1 + epsilon)Delta(2) for some epsilon > 1/polylog n, we show that it is even possible to compute a distance-2 coloring deterministically in polylog n time in the CONGEST model. Finally, we give a O(Delta(2) + log* n)-round deterministic CONGEST algorithm to compute distance-2 coloring with Delta(2) + 1 colors.
distributed multi-writer atomic registers are at the heart of a large number of distributed algorithms. While enjoying the benefits of atomicity, researchers further explore fast implementations of atomic reigsters wh...
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ISBN:
(纸本)9781450375825
distributed multi-writer atomic registers are at the heart of a large number of distributed algorithms. While enjoying the benefits of atomicity, researchers further explore fast implementations of atomic reigsters which are optimal in terms of data access latency. Though it is proved that multi-writer atomic register implementations are impossible when both read and write are required to be fast, it is still open whether implementations are impossible when only write or read is required to be fast. This work proves the impossibility of fast write implementations based on a series of chain arguments among indistiguishable executions. We also show the necessary and sufficient condition for fast read implementations by extending the results in the single-writer case. This work concludes a series of studies on fast implementations of distributed atomic registers.
A set of participants that want to agree on a common opinion despite the presence of malicious or Byzantine participants need to solve an instance of a Byzantine agreement problem. This classic problem has been well s...
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ISBN:
(纸本)9781450375825
A set of participants that want to agree on a common opinion despite the presence of malicious or Byzantine participants need to solve an instance of a Byzantine agreement problem. This classic problem has been well studied but most of the existing solutions assume that the participants are aware of n - the total number of participants in the system - and f - the upper bound on the number of Byzantine participants. In this paper, we examine a synchronous system with Byzantine faults where the participants are neither aware of n nor f. The participants have unique identifiers, which are not necessarily consecutive. For such a system, we give algorithms for rotor-coordinator and consensus, both with the resiliency of n > 3f, which is also the optimal resiliency for solving consensus when the participants know n and f. Thus, resiliency is unaffected even if the Byzantine participants can lie about n and f.
Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent ...
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ISBN:
(纸本)9781450375825
Locally checkable labeling problems (LCLs) are distributed graph problems in which a solution is globally feasible if it is locally feasible in all constant-radius neighborhoods. Vertex colorings, maximal independent sets, and maximal matchings are examples of LCLs. On the one hand, it is known that some LCLs benefit exponentially from randomness-for example, any deterministic distributed algorithm that finds a sinkless orientation requires Theta(logn) rounds in the LOCAL model, while the randomized complexity of the problem is Theta(log logn) rounds. On the other hand, there are also many LCLs in which randomness is useless. Previously, it was not known whether there are any LCLs that benefit from randomness, but only subexponentially. We show that such problems exist: for example, there is an LCL with deterministic complexity Theta(log(2) n) rounds and randomized complexity T(logn log logn) rounds.
This paper considers the problem of Byzantine fault-tolerance in distributed multi-agent optimization. In this problem, each agent has a local cost function. The goal of a distributed optimization algorithm is to allo...
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ISBN:
(纸本)9781450375825
This paper considers the problem of Byzantine fault-tolerance in distributed multi-agent optimization. In this problem, each agent has a local cost function. The goal of a distributed optimization algorithm is to allow the agents to collectively compute a minimum of their aggregate cost function. We consider the case when a certain number of agents may be Byzantine faulty. Such faulty agents may not follow a prescribed algorithm, and they may send arbitrary or incorrect information regarding their local cost functions. Unless a fault-tolerance mechanism is employed, traditional distributed optimization algorithms cannot tolerate such faulty agents. A reasonable goal in presence of faulty agents is to minimize the aggregate cost of the non-faulty agents. However, we show that this goal is impossible to achieve unless the cost functions of the non-faulty agents have a minimal redundancy property. We further propose a distributed optimization algorithm that allows the non-faulty agents to obtain a minimum of their aggregate cost if the minimal redundancy property holds. The scope of our algorithm is demonstrated through distributed sensing and learning applications, which are special cases of distributed optimization.
This paper proposes a framework called SnuRHAC, which provides an illusion of a single GPU for the multiple GPUs in a cluster. Under SnuRHAC, a CUDA program designed to use a single GPU can utilize multiple GPUs in a ...
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ISBN:
(纸本)9781450382175
This paper proposes a framework called SnuRHAC, which provides an illusion of a single GPU for the multiple GPUs in a cluster. Under SnuRHAC, a CUDA program designed to use a single GPU can utilize multiple GPUs in a cluster without any source code modification. SnuRHAC automatically distributes workload to multiple GPUs in a cluster and manages data across the nodes. To manage data efficiently, SnuRHAC extends CUDA Unified Memory and exploits its page fault mechanism. We also propose two prefetching techniques to fully exploit UM and to maximize performance. Static prefetching allows SnuRHAC to prefetch data by statically analyzing CUDA kernels. Dynamic prefetching complements static prefetching. SnuRHAC enforces an application to run on a single GPU if it is not suitable for multiple GPUs. We evaluate the performance of SnuRHAC using 18 benchmark applications from various sources. The evaluation result shows that while SnuRHAC significantly improves ease-of-programming, it shows scalable performance for the cluster environment depending on the application characteristics.
Parallel and distributedcomputing (PDC) has become pervasive in all aspects of computing, and thus it is essential that students include parallelism and distribution in the computational thinking that they apply to p...
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ISBN:
(纸本)9781450390712
Parallel and distributedcomputing (PDC) has become pervasive in all aspects of computing, and thus it is essential that students include parallelism and distribution in the computational thinking that they apply to problem solving, from the very beginning. Computer science education is still teaching to a 20th century model of algorithmic problem solving. Sequence, branch, and loop are taught in our early courses as the only organizing principles needed for algorithms, and we invest considerable time in showing how best to sequentially process large volumes of data. All computing devices that students use currently have multiple cores as well as GPU in many cases. Most of their favorite applications use multiple cores and numbers of distributed processors. Often concurrency offers simpler solutions than sequential approaches. acm and ABET have recommended including PDC in the undergraduate CS curriculum. However, we are still teaching them to solve problems using sequential thinking. In this workshop we overview the key PDC concepts and provide examples of how they may naturally be incorporated in early CS classes. We will introduce plugged and unplugged curriculum modules that have been successfully integrated in existing CS classes at multiple institutions. We will highlight the upcoming summer training that we are organizing, for which we have funding to support attendance.
Round-based models are very common message-passing models;combinatorial topology applied to distributedcomputing provides sweeping results like general lower bounds. We combine both to study the computability of k -s...
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ISBN:
(纸本)9781450375825
Round-based models are very common message-passing models;combinatorial topology applied to distributedcomputing provides sweeping results like general lower bounds. We combine both to study the computability of k -set agreement. Among all the possible round-based models, we consider oblivious ones, where the constraints are given only round per round by a set of allowed graphs. And among oblivious models, we focus on closed-above ones, that is models where the set of possible graphs contains all graphs with more edges than some starting graphs. These capture intuitively the underlying structure required by some communication model, like containing a ring. We then derive lower bounds and upper bounds in one round for k-set agreement, such that these bounds are proved using combinatorial topology but stated only in terms of graph properties. These bounds extend to multiple rounds when limiting our algorithms to be oblivious - recalling only pairs of processes and initial value, not who send what and when.
We present improved distributed algorithms for variants of the triangle finding problem in the model. We show that triangle detection, counting, and enumeration can be solved in rounds using expander decompositions. T...
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