Converting Online Algorithms to Local Computation Algorithms

Mansour, Yishay; Rubinstein, Aviad; Vardi, Shai; Xie, Ning

doi:10.1007/978-3-642-31594-7_55

Cited by 39 publications

(73 citation statements)

References 19 publications

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“…[MRVX12], showed that it is possible to transform any on-line algorithm on a graph of bounded degree (or whose degree is distributed binomially) to an LCA. The idea behind the reduction is simple: generate a random permutation on the vertices and simulate the on-line algorithm on this permutation.…”

Section: Theorem 62 [Mye81 At01]) the Allocation Algorithm A Admitmentioning

confidence: 99%

“…They show that, with high probability, this results in at most O(log n) queries. We require the following theorem from [MRVX12]. …”

Section: Theorem 62 [Mye81 At01]) the Allocation Algorithm A Admitmentioning

confidence: 99%

“…Claims 7.6 and 7.7 imply the following. Algorithm A U DU BV is a (O(log 4 n), O(log 3 n), 1/n) -LCA for maximal matching on graph of bounded degree k, by [MRVX12]. Notice, however, that we need to run A U DU BV once for calculating the allocation, and k more times for calculating the payment.…”

Section: Unit Demand Buyers Uniform-buyer-valuementioning

confidence: 99%

“…i therefore needs to recursively check the allocation of all agents that arrived before her, on which her allocation depends. As in [ARVX12,MRVX12], we model this using a query tree. We recall the following lemma from [MRVX12]: …”

Section: Random Serial Dictatorshipmentioning

confidence: 99%

“…1 2 -approximation to the maximum matching To obtain a 1 2 -approximation, we use the local greedy matching algorithm of [MRVX12], which we denote by A U DU V . Algorithm A U DU V simulates the well-known greedy on-line algorithm -as an edge arrives, it is added to the matching, if possible.…”

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confidence: 99%

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Local computation mechanism design

Hassidim

Mansour

Vardi

2014

Proceedings of the Fifteenth ACM Conference on Economics and Computation

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We introduce the notion of local computation mechanism design -designing game theoretic mechanisms that run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the replies to different queries are consistent with the same global feasible solution. When the mechanism employs payments, the computation of the payments is also done in polylogarithmic time and space. Furthermore, the mechanism needs to maintain incentive compatibility with respect to the allocation and payments.We present local computation mechanisms for a variety of classical game-theoretical problems: (1) stable matching, (2) job scheduling, (3) combinatorial auctions for unit-demand and k-minded bidders, and (4) the housing allocation problem.For stable matching, some of our techniques may have implications to the global (non-LCA) setting. Specifically, we show that when the men's preference lists are bounded, we can achieve an arbitrarily good approximation to the stable matching within a fixed number of iterations of the Gale-Shapley algorithm.

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Section: Theorem 62 [Mye81 At01]) the Allocation Algorithm A Admitmentioning

confidence: 99%

“…They show that, with high probability, this results in at most O(log n) queries. We require the following theorem from [MRVX12]. …”

Section: Theorem 62 [Mye81 At01]) the Allocation Algorithm A Admitmentioning

confidence: 99%

Section: Unit Demand Buyers Uniform-buyer-valuementioning

confidence: 99%

Section: Random Serial Dictatorshipmentioning

confidence: 99%

mentioning

confidence: 99%

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Local computation mechanism design

Hassidim

Mansour

Vardi

2014

Proceedings of the Fifteenth ACM Conference on Economics and Computation

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On giant components and treewidth in the layers model

Feige

Hermon²,

Reichman

2015

Random Struct Algorithms

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ABSTRACT:Given an undirected n-vertex graph G(V , E) and an integer k, let T k (G) denote the random vertex induced subgraph of G generated by ordering V according to a random permutation π and including in T k (G) those vertices with at most k −1 of their neighbors preceding them in this order. The distribution of subgraphs sampled in this manner is called the layers model with parameter k. The layers model has found applications in studying -degenerate subgraphs, the design of algorithms for the maximum independent set problem, and in bootstrap percolation.In the current work we expand the study of structural properties of the layers model. We prove that there are 3-regular graphs G for which with high probability T 3 (G) has a connected component of size (n), and moreover, T 3 (G) has treewidth (n). In contrast, T 2 (G) is known to be a forest (hence of treewidth 1), and we prove that if G is of bounded degree then with high probability the largest connected component in T 2 (G) is of size O(log n). We also consider the infinite grid Z 2 , for which we prove that T 4 (Z 2 ) contains a unique infinite connected component with probability 1.

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Constructing near spanning trees with few local inspections

Levi

Moshkovitz

Ron

et al. 2016

Random Struct Algorithms

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Constructing a spanning tree of a graph is one of the most basic tasks in graph theory.Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded-degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph G consisting of (1+ )n edges (for a prespecified constant > 0), where the decision for different edges should be consistent with the same subgraph G . Can this task be performed by inspecting only a constant number of edges in G? Our main results are:• We show that if every t-vertex subgraph of G has expansion 1/(log t) 1+o(1) then one can (deterministically) construct a sparse spanning subgraph G of G using few inspections. To this end we analyze a "local" version of a famous minimum-weight spanning tree algorithm.• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3-regular graphs of high girth, in which every t-vertex subgraph has expansion 1/(log t) 1−o(1) . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

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Converting Online Algorithms to Local Computation Algorithms

Cited by 39 publications

References 19 publications

Local computation mechanism design

Local computation mechanism design

On giant components and treewidth in the layers model

Constructing near spanning trees with few local inspections

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