We construct quasipolynomial-size proofs of the propositional pigeonhole principle in the deep inference system KS, addressing an open problem raised in previous works and matching the best known upper bound for the m...
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ISBN:
(纸本)9781450328869
We construct quasipolynomial-size proofs of the propositional pigeonhole principle in the deep inference system KS, addressing an open problem raised in previous works and matching the best known upper bound for the more general class of monotone proofs. We make significant use of monotone formulae computing boolean threshold functions, an idea previously considered in works of Atserias et al. The main construction, monotone proofs witnessing the symmetry of such functions, involves an implementation of merge-sort in the design of proofs in order to tame the structural behaviour of atoms, and so the complexity of normalization. Proof transformations from previous work on atomic flows are then employed to yield appropriate KS proofs. As further results we show that our constructions can be applied to provide quasipolynomial-size KS proofs of the parity principle and the generalized pigeonhole principle. These bounds are inherited for the class of monotone proofs, and we are further able to construct n(O(log log n))-size monotone proofs of the weak pigeonhole principle with (1 + epsilon)n pigeons and n holes for epsilon = 1= log(k) n, thereby also improving the best known bounds for monotone proofs.
In this paper, we study the interaction times of continuous distributed interactive computing in which the application states change due to not only user-initiated operations but also time passing. We formulate the Mi...
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ISBN:
(纸本)9781450320658
In this paper, we study the interaction times of continuous distributed interactive computing in which the application states change due to not only user-initiated operations but also time passing. We formulate the Minimum Interaction Time problem as a combinatorial problem of how the clients are assigned to the servers and the simulation time settings of the servers. We also outline two approaches to approximate the problem. Copyright 2013 acm.
A new model that depicts a network of randomized finite state machines operating in an asynchronous environment is introduced. This model, that can be viewed as a hybrid of the message passing model and cellular autom...
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ISBN:
(纸本)9781450320658
A new model that depicts a network of randomized finite state machines operating in an asynchronous environment is introduced. This model, that can be viewed as a hybrid of the message passing model and cellular automata is suitable for applying the distributedcomputing lens to the study of networks of sub-microprocessor devices, e.g., biological cellular networks and man-made nano-networks. Although the computation and communication capabilities of each individual device in the new model are, by design, much weaker than those of an abstract computer, we show that some of the most important and extensively studied distributedcomputing problems can still be solved efficiently. Copyright 2013 acm.
The proceedings contain 54 papers. The topics discussed include: distributedcomputing theory for wireless networks and mobile systems;pragmatic primitives for non-blocking data structures;the SkipTrie: low-depth conc...
ISBN:
(纸本)9781450320658
The proceedings contain 54 papers. The topics discussed include: distributedcomputing theory for wireless networks and mobile systems;pragmatic primitives for non-blocking data structures;the SkipTrie: low-depth concurrent search without rebalancing;optimal deterministic routing and sorting on the congested clique;Byzantine vector consensus in complete graphs;fast Byzantine agreement in dynamic networks;synchronous Byzantine agreement with nearly a cubic number of communication bits;how to meet asynchronously at polynomial cost;on the complexity of universal leader election;on the complexity of universal leader election;on minimum interaction time for continuous distributed interactive computing;scalable anonymous communication with Byzantine adversary;brokerage and closure in a strategic model of social capital;and feedback from nature: an optimal distributed algorithm for maximal independent set selection.
Numerous sophisticated local algorithm were suggested in the literature for various fundamental problems. Notable examples are the MIS and -coloring algorithms by Barenboim and Elkin (Distrib Comput 22(5-6):363-379, 2...
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ISBN:
(纸本)9781450307192
Numerous sophisticated local algorithm were suggested in the literature for various fundamental problems. Notable examples are the MIS and -coloring algorithms by Barenboim and Elkin (Distrib Comput 22(5-6):363-379, 2010), by Kuhn (2009), and by Panconesi and Srinivasan (J Algorithms 20(2):356-374, 1996), as well as the -coloring algorithm by Linial (J Comput 21:193, 1992). Unfortunately, most known local algorithms (including, in particular, the aforementioned algorithms) are non-uniform, that is, local algorithms generally use good estimations of one or more global parameters of the network, e.g., the maximum degree or the number of nodes . This paper provides a method for transforming a non-uniform local algorithm into a uniform one. Furthermore, the resulting algorithm enjoys the same asymptotic running time as the original non-uniform algorithm. Our method applies to a wide family of both deterministic and randomized algorithms. Specifically, it applies to almost all state of the art non-uniform algorithms for MIS and Maximal Matching, as well as to many results concerning the coloring problem (In particular, it applies to all aforementioned algorithms). To obtain our transformations we introduce a new distributed tool called pruning algorithms, which we believe may be of independent interest.
The distributed systems research community has developed many provably correct algorithms and abstractions that are in wide use. However, practical implementations of distributed systems often contain many bugs, and p...
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ISBN:
(纸本)9781450320658
The distributed systems research community has developed many provably correct algorithms and abstractions that are in wide use. However, practical implementations of distributed systems often contain many bugs, and practitioners spend much of their time troubleshooting these bugs. In this paper we present an algorithm, retrospective causal inference, to ease the burden of troubleshooting. We end by enumerating several open research problems related to the troubleshooting process. Copyright 2013 acm.
The M-renaming task requires n+1 processes, each starting with a unique input name (from an arbitrary large range), to coordinate the choice of new output names from a range of size M. This paper presents the first up...
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ISBN:
(纸本)9781450320658
The M-renaming task requires n+1 processes, each starting with a unique input name (from an arbitrary large range), to coordinate the choice of new output names from a range of size M. This paper presents the first upper bound on the complexity of hard renaming, i.e., 2n-renaming, when n + 1 is not a prime power. It is known that 2n-renaming can be solved if and only if n+1 is not a prime power;however, the previous proof of the "if" part was non-constructive, involving an approximation theorem;in particular, it did not yield a concrete upper bound on the complexity of the resulting protocol. Copyright 2013 acm.
We study the edge-coloring problem in the message-passing model of distributedcomputing. This is one of the most fundamental problems in this area. Currently, the best-known deterministic algorithms for (2 Delta -1)-...
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ISBN:
(纸本)9781450307192
We study the edge-coloring problem in the message-passing model of distributedcomputing. This is one of the most fundamental problems in this area. Currently, the best-known deterministic algorithms for (2 Delta -1)-edge-coloring requires O(Delta) + log* n time (Panconesi and Rizzi in Distrib Comput 14(2):97-100, 2001), where Delta is the maximum degree of the input graph. Also, recent results of Barenboim and Elkin (2010) for vertex-coloring imply that one can get an O(Delta)-edge-coloring in time, and an -edge-coloring in O(log Delta log n) time, for an arbitrarily small constant . In this paper we devise a significantly faster deterministic edge-coloring algorithm. Specifically, our algorithm computes an O(Delta)-edge-coloring in time, and an -edge-coloring in O(log Delta) + log* n time. This result improves the state-of-the-art running time for deterministic edge-coloring with this number of colors in almost the entire range of maximum degree Delta. Moreover, it improves it exponentially in a wide range of Delta, specifically, for 2 (Omega(log*n)) a parts per thousand currency sign Delta a parts per thousand currency sign polylog(n). In addition, for small values of Delta (up to log(1 - delta) n, for some fixed delta > 0) our deterministic algorithm outperforms all the existing randomized algorithms for this problem. Also, our algorithm is the first O(Delta)-edge-coloring algorithm that has running time o(Delta) + log* n, for the entire range of Delta. All previous (deterministic and randomized) O(Delta)-edge-coloring algorithms require time. On our way to these results we study the vertex-coloring problem on graphs with bounded neighborhood independence. This is a large family of graphs, which strictly includes line graphs of r-hypergraphs (i.e., hypergraphs in which each hyperedge contains r or less vertices) for r = O(1), and graphs of bounded growth. We devise a very fast deterministic algorithm for vertex-coloring graphs with bounded neighborhood independe
This paper shows for the first time that distributedcomputing can be both reliable and efficient in an environment that is both highly dynamic and hostile. More specifically, we show how to maintain clusters of size ...
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ISBN:
(纸本)9781450320658
This paper shows for the first time that distributedcomputing can be both reliable and efficient in an environment that is both highly dynamic and hostile. More specifically, we show how to maintain clusters of size O(log N), each containing more than two thirds of honest nodes with high probability, within a system whose size can vary polyno-mially with respect to its initial size. Furthermore, the communication cost induced by each node arrival or departure is polylogarithmic with respect to N, the maximal size of the system. Our clustering can be achieved despite the presence of a Byzantine adversary controlling a fraction τ ≤ 1/3 - e of the nodes, for some fixed constant e > 0, independent of N. So far, such a clustering could only be performed for systems whose size can vary constantly and it was not clear whether that was at all possible for polynomial variances. Copyright 2013 acm.
Maximal Independent Set selection is a fundamental problem in distributedcomputing. A novel probabilistic algorithm for this problem has recently been proposed by Afek et al, inspired by the study of the way that dev...
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ISBN:
(纸本)9781450320658
Maximal Independent Set selection is a fundamental problem in distributedcomputing. A novel probabilistic algorithm for this problem has recently been proposed by Afek et al, inspired by the study of the way that developing cells in the fly become specialised. The algorithm they propose is simple and robust, but not as efficient as previous approaches: the expected time complexity is O(log2 n). Here we first show that the approach of Afek et al cannot achieve better efficiency than this across all networks, no matter how the global probability values are chosen. However, we then propose a new algorithm that incorporates another important feature of the biological system: the probability value at each node is adapted using local feedback from neighbouring nodes. Our new algorithm retains all the advantages of simplicity and robustness, but also achieves the optimal efficiency of O(log n) expected time. The new algorithm also has only a constant message complexity per node.
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