How Much Memory Is Needed for Leader Election

Fusco, Emanuele G.; Pełc, Andrzej

doi:10.1007/978-3-642-15763-9_25

Cited by 7 publications

(6 citation statements)

References 36 publications

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“…They proved that O(n) bits of advice allow to obtain constant time in such networks, while o(n) bits are not enough. Distributed computation on anonymous networks has been investigated by many authors, e.g., [2,3,6,12,13,19,25,27,31] for problems ranging from leader election to computing boolean functions and communication in wireless networks. In [12] the authors compared randomized and deterministic algorithms to solve distributed problems in anonymous networks.…”

Section: Related Workmentioning

confidence: 99%

Topology recognition with advice

Fusco

Pełc

Petreschi

2016

Information and Computation

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In topology recognition, each node of an anonymous network has to deterministically produce an isomorphic copy of the underlying graph, with all ports correctly marked. This task is usually unfeasible without any a priori information. Such information can be provided to nodes as advice. An oracle knowing the network can give a (possibly different) string of bits to each node, and all nodes must reconstruct the network using this advice, after a given number of rounds of communication. During each round each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations. The time of completing topology recognition is the number of rounds it takes, and the size of advice is the maximum length of a string given to nodes.We investigate tradeoffs between the time in which topology recognition is accomplished and the minimum size of advice that has to be given to nodes. We provide upper and lower bounds on the minimum size of advice that is sufficient to perform topology recognition in a given time, in the class of all graphs of size n and diameter D ≤ αn, for any constant α < 1. In most cases, our bounds are asymptotically tight.

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Section: Related Workmentioning

confidence: 99%

Topology recognition with advice

Fusco

Pełc

Petreschi

2016

Information and Computation

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“…In [19,21], the authors studied message complexity of leader election in rings with possibly nonunique labels. Memory needed for leader election in unlabeled networks was studied in [23]. In [16], the authors investigated the feasibility of leader election among anonymous agents that navigate in a network in an asynchronous way.…”

Section: Related Workmentioning

confidence: 99%

Deterministic Leader Election in Anonymous Radio Networks

Miller¹,

Pełc²,

Yadav³

2020

Preprint

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Leader election is a fundamental task in distributed computing. It is a symmetry breaking problem, calling for one node of the network to become the leader, and for all other nodes to become non-leaders. We consider leader election in anonymous radio networks modeled as simple undirected connected graphs. Nodes communicate in synchronous rounds. In each round, a node can either transmit a message to all its neighbours, or stay silent and listen. A node v hears a message from a neighbour w in a given round if v listens in this round and if w is its only neighbour transmitting in this round. If v listens in a round in which more than one neighbour transmits then v hears noise that is different from any message and different from silence.We assume that nodes are identical (anonymous) and execute the same deterministic algorithm. Under this scenario, symmetry can be broken only in one way: by different wake-up times of the nodes. In which situations is it possible to break symmetry and elect a leader using time as symmetry breaker? In order to answer this question, we consider configurations. A configuration is the underlying graph with nodes tagged by non-negative integers with the following meaning. A node can either wake up spontaneously in the round shown on its tag, according to some global clock, or can be woken up hearing a message sent by one of its already awoken neighbours. The local clock of a node starts at its wakeup and nodes do not have access to the global clock determining their tags. A configuration is feasible if there exists a distributed algorithm that elects a leader for this configuration.Our main result is a complete algorithmic characterization of feasible configurations. More precisely, we design a centralized decision algorithm, working in polynomial time, whose input is a configuration and which decides if the configuration is feasible. Using this algorithm we also provide a dedicated deterministic distributed leader election algorithm for each feasible configuration that elects a leader for this configuration in time O(n 2 σ), where n is the number of nodes and σ is the difference between the largest and smallest tag of the configuration. We then ask the question if there exists a universal deterministic distributed algorithm electing a leader for all feasible configurations. The answer turns out to be no, and we show that such a universal algorithm cannot exist even for the class of 4-node feasible configurations. We also prove that a distributed version of our decision algorithm cannot exist.

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“…Characterizations of feasible instances for leader election and naming problems have been provided in [10,12,13]. Memory needed for leader election in unlabeled networks has been studied in [21]. In [22], the authors investigated the time of leader election in anonymous networks by characterizing this time in terms of the size and diameter of the network, and of an additional parameter, called level of symmetry, which measures how deeply nodes have to inspect the network to notice differences in their views of it.…”

Section: Related Workmentioning

confidence: 99%

Topology recognition and leader election in colored networks

Dereniowski

Pełc

2016

Theoretical Computer Science

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Topology recognition and leader election are fundamental tasks in distributed computing in networks. The first of them requires each node to find a labeled isomorphic copy of the network, while the result of the second one consists in a single node adopting the label 1 (leader), with all other nodes adopting the label 0 and learning a path to the leader. We consider both these problems in networks whose nodes are equipped with not necessarily distinct labels called colors, and ports at each node of degree d are arbitrarily numbered 0, 1, . . . , d − 1. Colored networks are generalizations both of labeled networks, in which nodes have distinct labels, and of anonymous networks, in which nodes do not have labels (all nodes have the same color).In colored networks, topology recognition and leader election are not always feasible. Hence we study two more general problems. Consider a colored network and an input I given to its nodes. The aim of the problem TOP, for this colored network and for I, is to solve topology recognition in this network, if this is possible under input I, and to have all nodes answer "unsolvable" otherwise. Likewise, the aim of the problem LE is to solve leader election in this network, if this is possible under input I, and to have all nodes answer "unsolvable" otherwise.We show that nodes of a network can solve problems TOP and LE, if they are given, as input I, an upper bound k on the number of nodes of a given color, called the size of this color. On the other hand we show that, if the nodes are given an input that does not bound the size of any color, then the answer to TOP and LE must be "unsolvable", even for the class of rings.Under the assumption that nodes are given an upper bound k on the size of a given color, we study the time of solving problems TOP and LE in the LOCAL model in which, during each round, each node can exchange arbitrary messages with all its neighbors and perform arbitrary local computations. We give an algorithm to solve each of these problems in arbitrary networks in time O(kD + D log(n/D)), where D is the diameter of the network and n is its size. We also show that this time is optimal, by exhibiting classes of networks in which every algorithm solving problems TOP or LE must use time Ω(kD + D log(n/D)).

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How Much Memory Is Needed for Leader Election

Cited by 7 publications

References 36 publications

Topology recognition with advice

Topology recognition with advice

Deterministic Leader Election in Anonymous Radio Networks

Topology recognition and leader election in colored networks

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