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Local Distributed Decision
 In FOCS 2011
"... A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Despite considerable progress, research efforts in this direction have not yet resulted in a solid basis in the form of a fundamental computational complexity theory for locality. Inspired ..."
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Cited by 17 (11 self)
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A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Despite considerable progress, research efforts in this direction have not yet resulted in a solid basis in the form of a fundamental computational complexity theory for locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of locality, solving a decision problem requires the processors to independently inspect their local neighborhoods and then collectively decide whether a given global input instance belongs to some specified language. We consider the standard LOCAL model of computation and define LD(t) (for local decision) as the class of decision problems that can be solved in t communication rounds. We first study the intriguing question of whether randomization helps in local distributed computing, and to what extent. Specifically, we define the corresponding randomized class BPLD(t, p, q), containing all languages for which there exists a randomized algorithm that runs in t rounds, accepts correct instances with probability at least p and rejects incorrect ones with probability at least q. We show that p 2 +q = 1 is a threshold for the containment of LD(t) in BPLD(t, p, q). More precisely, we show that there exists a language that does not belong to LD(t) for any t = o(n) but does belong to BPLD(0, p, q) for any p, q ∈ (0, 1] such that p 2 +q ≤ 1. On the other hand, we show that, restricted to
Collaborative Search on the Plane Without Communication
 In Proceedings of the 31st ACM Symposium on Principles of Distributed Computing (PODC
, 2012
"... We use distributed computing tools to provide a new perspective on the behavior of cooperative biological ensembles. We introduce the Ants Nearby Treasure Search (ANTS) problem, a generalization of the classical cowpath problem [10, 20, 41, 42], which is relevant for collective foraging in animal g ..."
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Cited by 8 (1 self)
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We use distributed computing tools to provide a new perspective on the behavior of cooperative biological ensembles. We introduce the Ants Nearby Treasure Search (ANTS) problem, a generalization of the classical cowpath problem [10, 20, 41, 42], which is relevant for collective foraging in animal groups. In the ANTS problem, k identical (probabilistic) agents, initially placed at some central location, collectively search for a treasure in the twodimensional plane. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the distance between the central location and the target. This is biologically motivated by cooperative, central place foraging, such as performed by ants around their nest. In this type of search there is a strong preference to locate nearby food sources before those that are further away. We focus on trying to find what can be achieved if communication is limited or altogether absent. Indeed, to avoid overlaps agents must be highly dispersed making communication difficult. Furthermore, if the agents do not commence the search in synchrony, then even initial communication is problematic. This holds, in particular, with respect to the question
Locality and Checkability in Waitfree Computing
"... Abstract. This paper studies several notions of locality that are inherent to the specification of distributed tasks and independent of the computing environment, and investigates the ability of a shared memory waitfree system to solve tasks satisfying various forms of locality. First, we define a ..."
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Cited by 8 (7 self)
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Abstract. This paper studies several notions of locality that are inherent to the specification of distributed tasks and independent of the computing environment, and investigates the ability of a shared memory waitfree system to solve tasks satisfying various forms of locality. First, we define a task to be projectionclosed if every partial output pi(t) for a full input s is also a valid output for the partial input pi(s) and prove that projectionclosed tasks are precisely those tasks that are waitfree checkable. Our second main contribution is dealing with a stronger notion of locality of topological nature. A task T = (I,O,∆) is said to be localitypreserving if and only if O is a covering complex of I, that is, each simplex s of I is mapped by ∆ to a set of simplexes of O each isomorphic to s. This topological property yields obstacles for waitfree solvability different in nature from the classical agreement impossibility results. On the other hand, localitypreserving tasks are projectionclosed and therefore always waitfree checkable. We provide a classification of localitypreserving tasks in term of their computational power, by establishing a correspondence between localitypreserving tasks and subgroups of the edgepath group of a complex. Using this correspondence, we prove the existence of hierarchies of localitypreserving tasks, each one containing a universal task (induced by the universal covering complex), and at the bottom the trivial identity task.
On the Impact of Identifiers on Local Decision
"... The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that are inherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2) topological information gathering. In the context of local c ..."
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Cited by 7 (5 self)
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The issue of identifiers is crucial in distributed computing. Informally, identities are used for tackling two of the fundamental difficulties that are inherent to deterministic distributed computing, namely: (1) symmetry breaking, and (2) topological information gathering. In the context of local computation, i.e., when nodes can gather information only from nodes at bounded distances, some insight regarding the role of identities has been established. For instance, it was shown that, for large classes of construction problems, the role of the identities can be rather small. However, for the identities to play no role, some other kinds of mechanisms for breaking symmetry must be employed, such as edgelabeling or sense of direction. When it comes to local distributed decision problems, the specification of the decision task does not seem to involve symmetry breaking. Therefore, it is expected that, assuming nodes can gather sufficient information about their neighborhood, one could get rid of the identities, without employing extra mechanisms for breaking symmetry.
Memory lower bounds for randomized collaborative search and implications for biology
 In Distributed Computing
, 2012
"... Abstract. Initial knowledge regarding group size can be crucial for collective performance. We study this relation in the context of the Ants Nearby Treasure Search (ANTS) problem [18], which models natural cooperative foraging behavior such as that performed by ants around their nest. In this pro ..."
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Cited by 6 (2 self)
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Abstract. Initial knowledge regarding group size can be crucial for collective performance. We study this relation in the context of the Ants Nearby Treasure Search (ANTS) problem [18], which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k (probabilistic) agents, initially placed at some central location, collectively search for a treasure on the twodimensional grid. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the (unknown) distance between the central location and the target. It is easy to see that T = Ω(D+D2/k) time units are necessary for finding the treasure. Recently, it has been established that O(T) time is sufficient if the agents know their total number k (or a constant approximation of it), and enough memory bits are available at their disposal [18]. In this paper, we establish lower bounds on the agent memory size required for achieving certain running time performances. To the best our knowledge, these bounds are the first nontrivial lower bounds for the memory size of probabilistic searchers. For example, for every given positive constant , terminating the search by time O(log1− k · T) requires agents to use Ω(log log k) memory bits. From a high level perspective, we illustrate how methods from distributed computing can be useful in generating lower bounds for cooperative biological ensembles. Indeed, if experiments that comply with our setting reveal that the ants ’ search is time efficient, then our theoretical lower bounds can provide some insight on the memory ants use for this task.
Randomized Distributed Decision
"... Abstract. The paper tackles the power of randomization in the context of locality by analyzing the ability to “boost ” the success probability of deciding a distributed language. The main outcome of this analysis is that the distributed computing setting contrasts significantly with the sequential o ..."
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Cited by 6 (4 self)
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Abstract. The paper tackles the power of randomization in the context of locality by analyzing the ability to “boost ” the success probability of deciding a distributed language. The main outcome of this analysis is that the distributed computing setting contrasts significantly with the sequential one as far as randomization is concerned. Indeed, we prove that in some cases, the ability to increase the success probability for deciding distributed languages is rather limited. We focus on the notion of a (p, q)decider for a language L, which is a distributed randomized algorithm that accepts instances in L with probability at least p and rejects instances outside of L with probability at least q. It is known that every hereditary language that can be decided in t rounds by a (p, q)decider, where p 2 + q> 1, can be decided deterministically in O(t) rounds. One of our results gives evidence supporting the conjecture that the above statement holds for all distributed languages and not only for hereditary ones, by proving the conjecture for
What can be decided locally without identifiers
 In Proc. 32nd ACM Symp. on Principles of Distributed Computing
, 2013
"... Abstract. Do unique node identifiers help in deciding whether a network G has a prescribed property P? We study this question in the context of distributed local decision, where the objective is to decide whether G ∈ P by having each node run a constanttime distributed decision algorithm. If G ∈ P, ..."
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Cited by 3 (2 self)
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Abstract. Do unique node identifiers help in deciding whether a network G has a prescribed property P? We study this question in the context of distributed local decision, where the objective is to decide whether G ∈ P by having each node run a constanttime distributed decision algorithm. If G ∈ P, all the nodes should output yes; if G / ∈ P, at least one node should output no. A recent work (Fraigniaud et al., OPODIS 2012) studied the role of identifiers in local decision and gave several conditions under which identifiers are not needed. In this article, we answer their original question. More than that, we do so under all combinations of the following two critical variations on the underlying model of distributed computing: − (B): the size of the identifiers is bounded by a function of the size of the input network; as opposed to (¬B): the identifiers are unbounded. − (C): the nodes run a computable algorithm; as opposed to (¬C): the nodes can compute any, possibly uncomputable function. While it is easy to see that under (¬B,¬C) identifiers are not needed, we show that under all other combinations there are properties that can be decided locally if and only if identifiers are present. Our constructions use ideas from classical computability theory.
Towards a Complexity Theory for Local Distributed Computing
, 2013
"... A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Yet despite considerable progress, research efforts in this direction have not yet resulted in a solid basis in the form of a fundamental computational complexity theory for locality. Insp ..."
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Cited by 2 (0 self)
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A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Yet despite considerable progress, research efforts in this direction have not yet resulted in a solid basis in the form of a fundamental computational complexity theory for locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of locality, solving a decision problem requires the processors to independently inspect their local neighborhoods and then collectively decide whether a given global input instance belongs to some specified language. We consider the standard LOCAL model of computation and define LD(t) (for local decision) as the class of decision problems that can be solved in t communication rounds. We first study the intriguing question of whether randomization helps in local distributed computing, and to what extent. Specifically, we define the corresponding randomized class BPLD(t, p, q), containing all languages for which there exists a randomized algorithm that runs in t rounds, accepts correct instances with probability at least p, and rejects incorrect ones with probability at least q. We
Randomized Distributed Decision Pierre Fraigniaud∗ ‡ Mika Göös † Amos Korman∗
"... The paper tackles the power of randomization in the context of local distributed computing by analyzing the ability to “boost ” the success probability of deciding a distributed language using a MonteCarlo algorithm. We prove that, in many cases, the ability to increase the success probability for ..."
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The paper tackles the power of randomization in the context of local distributed computing by analyzing the ability to “boost ” the success probability of deciding a distributed language using a MonteCarlo algorithm. We prove that, in many cases, the ability to increase the success probability for deciding distributed languages is rather limited. This contrasts with the sequential computing setting where boosting can systematically be achieved by repeating the randomized execution.