Fast distributed construction of <i>k</i>-dominating sets and applications

Kutten, Shay; Peleg, David

doi:10.1145/224964.224990

Cited by 131 publications

(282 citation statements)

References 21 publications

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“…However, the authors missed one special case, which unfortunately invalidates their proof for some networks. The same flaw is present in some subsequent papers [25,27]. Ravelomanana [28] gives a randomized algorithm designed for synchronous UDG networks whose time complexity is O(D) rounds.…”

Section: Related Workmentioning

confidence: 66%

“…However, the proof given in [26] overlooked a special case. The same case was overlooked in some other subsequent papers as well [25,27].…”

Section: Boundmentioning

confidence: 92%

“…There exist several non self-stabilizing distributed solutions for finding a k-dominating set in a network [26,25,1,18,28]. Deterministic solutions given in [1,18] are designed for asynchronous mobile ad hoc networks, i.e., they assume networks with a Unit Disk Graph (UDG) topology.…”

Section: Related Workmentioning

confidence: 99%

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Self-Stabilizing Small k-Dominating Sets

Datta¹,

Larmore²,

Devismes

et al. 2013

IJNC

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A self-stabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, causes the system to recover in finite time without external (e.g., human) intervention. In this paper, we give a distributed asynchronous silent self-stabilizing algorithm for finding a minimal k-dominating set of at most n k+1 processes in an arbitrary identified network of size n. We give a transformer that allows our algorithm to work under an unfair daemon, the weakest scheduling assumption. The complexity of our solution is O(n) rounds and O(Dn 3 ) steps using O(log k + log n + k log N k ) bits per process, where D is the diameter of the network and N is an upper bound on n.

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Section: Related Workmentioning

confidence: 66%

“…However, the proof given in [26] overlooked a special case. The same case was overlooked in some other subsequent papers as well [25,27].…”

Section: Boundmentioning

confidence: 92%

See 1 more Smart Citation

Self-Stabilizing Small k-Dominating Sets

Datta¹,

Larmore²,

Devismes

et al. 2013

IJNC

View full text Add to dashboard Cite

show abstract

“…The asynchrony of the computational entities means that the algorithm must work regardless of the time required for each computation or movement, which is finite but a priori unknown (i.e., determined by an adversary); however, the time complexity of the algorithm is measured only over those executions where time delays are unitary (i.e., determined by a synchronous scheduler), as traditional in distributed computing (e.g., [12,18,23]). …”

Section: Main Contributionsmentioning

confidence: 99%

“…The amount of time between the earliest start time of the protocol by any agent and the time all the agents that started the protocol have terminated the execution of protocol. Since the system is asynchronous, when evaluating the time complexity we will employ ideal time; i.e., we will assume that it time delays are unitary (e.g., see [12,18,23]). …”

Section: Definitions and Notationsmentioning

confidence: 99%

Time Optimal Algorithms for Black Hole Search in Rings

Balamohan

Flocchini

Miri

et al. 2010

Combinatorial Optimization and Applications

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Abstract. In a network environments supporting mobile entities (called robots or agents), a black hole is harmful site that destroys any incoming entity without leaving any visible trace. The black-hole search problem is the task of a team of k > 1 mobile entities, starting from the same safe location and executing the same algorithm, to determine within finite time the location of the black hole. In this paper we consider the black hole search problem in asynchronous ring networks of n nodes, and focus on the time complexity. It is known that any algorithm for black-hole search in a ring requires at least 2(n − 2) time in the worst case. The best algorithm achieves this bound with a team of n − 1 agents with an average time cost 2(n − 2), equal to the worst case. In this paper we first show how the same number of agents using 2 extra time units from optimal in the worst case, can solve the problem in only 7 4 n − O(1) time on the average. We then prove that the optimal average case complexity 3 2 n − O(1) can be achieved without increasing the worst case using 2(n − 1) agents Finally we design an algorithm that achieves asymptotically optimal both worst case and average case time complexity employing an optimal team of k = 2 agents, thus improving on the earlier results that required O(n) agents.

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Randomized greedy algorithms for finding smallk-dominating sets of regular graphs

Duckworth

Mans

2005

Random Struct. Alg.

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ABSTRACT:A k-dominating set of a graph G is a subset D of the vertices of G such that every vertex of G is either in D or at distance at most k from a vertex in D. It is of interest to find kdominating sets of small cardinality. In this paper we consider simple randomized greedy algorithms for finding small k-dominating sets of regular graphs. We analyze the average-case performance of the most efficient of these simple heuristics showing that it performs surprisingly well on average. The analysis is performed on random regular graphs using differential equations. This, in turn, proves upper bounds on the size of a minimum k-dominating set of random regular graphs.

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Fast distributed construction of k-dominating sets and applications

Cited by 131 publications

References 21 publications

Self-Stabilizing Small k-Dominating Sets

Self-Stabilizing Small k-Dominating Sets

Time Optimal Algorithms for Black Hole Search in Rings

Randomized greedy algorithms for finding smallk-dominating sets of regular graphs

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