Distributed backup placement in networks

Halldórsson, Magnús M.; Köhler, Sven; Patt-Shamir, Boaz; Rawitz, Dror

doi:10.1007/s00446-017-0299-x

Cited by 12 publications

(31 citation statements)

References 29 publications

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“…In the distributed setting, this problem is called Backup Placement. It was introduced by Halldorsson, Kohler, Patt-Shamir, and Rawitz [8]. It is very well motivated by computer networks whose nodes may have memory faults, and wish to store backup copies of their data at neighboring nodes [11].…”

Section: Introductionmentioning

confidence: 99%

“…The bestcurrently known solution is a randomized algorithm with running time O( log 6 n log 4 log n ) that obtains an approximation factor of O( log n log log n ). This solution due to Halldorsen et al [8] is non-trivial at all, and involves distributed computations of a certain variant of matching, called an f -matching, in bipartite graphs. On the other hand, in certain network topologies, simpler and much more efficient solutions are known.…”

Section: Introductionmentioning

confidence: 99%

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Distributed Backup Placement in One Round and its Applications to Maximum Matching Approximation and Self-Stabilization

Barenboim¹,

Oren²

2020

Symposium on Simplicity in Algorithms

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In the distributed backup-placement problem [8] each node of a network has to select one neighbor, such that the maximum number of nodes that make the same selection is minimized. This is a natural relaxation of the perfect matching problem, in which each node is selected just by one neighbor. Previous (approximate) solutions for backup placement are non-trivial, even for simple graph topologies, such as dense graphs [5]. In this paper we devise an algorithm for dense graph topologies, including unit disk graphs, unit ball graphs, line graphs, graphs with bounded diversity, and many more. Our algorithm requires just one round, and is as simple as the following operation. Consider a circular list of neighborhood IDs, sorted in an ascending order, and select the ID that is next to the selecting vertex ID. Surprisingly, such a simple one-round strategy turns out to be very efficient for backup placement computation in dense networks. Not only that it improves the number of rounds of the solution, but also the approximation ratio is improved by a multiplicative factor of at least 2.Our new algorithm has several interesting implications. In particular, it gives rise to a (2 + ǫ)approximation to maximum matching within O(log * n) rounds in dense networks. The resulting algorithm is very simple as well, in sharp contrast to previous algorithms that compute such a solution within this running time. Moreover, these algorithms are applicable to a narrower graph family than our algorithm. For the same graph family, the best previously-known result has O(log ∆ + log * n) running time [4]. Another interesting implication is the possibility to execute our backup placement algorithm as-is in the self-stabilizing setting. This makes it possible to simplify and improve other algorithms for the self-stabilizing setting, by employing helpful properties of backup placement.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed Backup Placement in One Round and its Applications to Maximum Matching Approximation and Self-Stabilization

Barenboim¹,

Oren²

2020

Symposium on Simplicity in Algorithms

View full text Add to dashboard Cite

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“…Finding a backup placement in a network while minimizing the load on the network vertices is a very important goal [12,13,23]. First of all, it allows each vertex to perform a backup to a neighboring node, rather than a more distant destination, and thus improves network performance.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, if a certain node fails, the number of backups that become unavailable is minimized. For these and other reasons, the backup placement problem is considered as a central distributed problem by Halldorsson, Kohler, Patt-Shamir and Rawitz [12], who initiated the study of this problem in the distributed setting in 2015.…”

Section: Introductionmentioning

confidence: 99%

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Fast Distributed Backup Placement in Sparse and Dense Networks

Barenboim¹,

Oren²

2020

Symposium on Algorithmic Principles of Computer Systems

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We consider the Backup Placement problem in networks in the CON GEST distributed setting. Given a network graph G = (V, E), the goal of each vertex v ∈ V is selecting a neighbor, such that the maximum number of vertices in V that select the same vertex is minimized. The backup placement problem was introduced by Halldorsson, Kohler, Patt-Shamir, and Rawitz [12], who obtained an O(log n/ log log n) approximation with randomized polylogarithmic time. Their algorithm remained the state-of-the-art for general graphs, as well as specific graph topologies. In this paper we obtain significantly improved algorithms for various graph topologies. Specifically, we show that O(1)-approximation to optimal backup placement can be computed deterministically in O(1) rounds in graphs that model wireless networks, certain social networks, claw-free graphs, and more generally, in any graph with neighborhood independence bounded by a constant. At the other end, we consider sparse graphs, such as trees, forests, planar graphs and graphs of constant arboricity, and obtain a constant approximation to optimal backup placement in O(log n) deterministic rounds.Clearly, our constant-time algorithms for graphs with constant neighborhood independence are asymptotically optimal. Moreover, we show that our algorithms for sparse graphs are not far from optimal as well, by proving several lower bounds. Specifically, optimal backup placement of unoriented trees requires Ω(log n) time, and approximate backup placement with a polylogarithmic approximation factor requires Ω( log n/ log log n) time. Our results extend the knowledge regarding the question of "what can be computed locally?" [20], and reveal surprising gaps between complexities of distributed symmetry breaking problems.

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