We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees in the usual LOCAL model of distributedcomputing. These are loca...
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ISBN:
(纸本)9781450375825
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees in the usual LOCAL model of distributedcomputing. These are locally checkable problems that can be encoded with an alphabet of size two in the edge labeling formalism. Examples of binary labeling problems include sinkless orientation, sinkless and sourceless orientation, 2-vertex coloring, and perfect matching. We show that the complexity of any such problem is in one of the following classes: O(1), Theta(log n), Theta(n), or unsolvable. Furthermore, given the description of any binary labeling problem, we can easily determine in which of the four classes it is and what is an asymptotically optimal algorithm for solving it.
The problem of coloring the edges of an n-node graph of maximum degree. with 2 Delta - 1 colors is one of the key symmetry breaking problems in the area of distributed graph algorithms. While there has been a lot of p...
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ISBN:
(纸本)9781450375825
The problem of coloring the edges of an n-node graph of maximum degree. with 2 Delta - 1 colors is one of the key symmetry breaking problems in the area of distributed graph algorithms. While there has been a lot of progress towards the understanding of this problem, the dependency of the running time on. has been a long-standing open question. Very recently, Kuhn [SODA '20] showed that the problem can be solved in time 2O(root log Delta) + O(log* n). In this paper, we study the edge coloring problem in the distributed LOCAL model. We show that the (degree + 1)-list edge coloring problem, and thus also the (2 Delta- 1)-edge coloring problem, can be solved deterministically in time 2(O(log2 log Delta))+ O(log* n). This is a significant improvement over the result of Kuhn [SODA '20].
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.
The Advanced Placement Computer Science principles (AP CSP) curriculum framework has been in use since 2016. The AP CSP framework has leveraged the use of computational thinking skills to scaffold students into unders...
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ISBN:
(纸本)9781450394338
The Advanced Placement Computer Science principles (AP CSP) curriculum framework has been in use since 2016. The AP CSP framework has leveraged the use of computational thinking skills to scaffold students into understanding a variety of computing topics spread throughout the content of the curriculum. This Lightning Talk explores ideas for future work with high school AP CSP teachers in developing culturally relevant and sustaining (CR-S) curriculum to strengthen the efforts of broadening participation among Black, Indigenous, and other students of color in AP CSP courses. To do this, this work approaches culturally relevant and sustaining computing strategies as valuable tools to integrate into the AP CSP curriculum, classroom environments, and teachers' pedagogical approaches. This work looks to the Ghanaian practices of adinkra cloth making as a computationally rich cultural practice that can support student learning. The history and cultural practices surrounding Adinkra reveal richly developed, embedded mathematical and algorithmic knowledge, that is relevant to several AP CSP units. The talk described here explains how Adinkra artisans use ?heritage algorithms" to accomplish the task of creating adinkra cloth. Framing the adinkra process this way has implications for teaching and learning computing as well as broadening participation.
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