Coordination mechanisms

Christodoulou, George; Koutsoupias, Elias; Nanavati, Akash

doi:10.1016/j.tcs.2009.01.005

Cited by 119 publications

(52 citation statements)

References 39 publications

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“…However they lack an important aspect of real network routing which is the fact that routing happens over time, and any realistic model should take this into account. To address this issue, several new models have been proposed to capture the nature of realistic routing over time [10,11,21,19,24,13,12,4]. Amongst these models, the concept of coordination mechanisms, first introduced in an influential paper by Christodoulou, Koutsoupias, and Nanavati [10], have been proposed to capture the queueing nature of routing.…”

Section: Introductionmentioning

confidence: 99%

“…To address this issue, several new models have been proposed to capture the nature of realistic routing over time [10,11,21,19,24,13,12,4]. Amongst these models, the concept of coordination mechanisms, first introduced in an influential paper by Christodoulou, Koutsoupias, and Nanavati [10], have been proposed to capture the queueing nature of routing. Coordination mechanisms model the decentralized nature of routing decisions made by machines and the selfish behavior of jobs: they do so by seeking local policies that achieve a good price of anarchy in the resulting equilibria in a corresponding game.…”

Section: Introductionmentioning

confidence: 99%

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Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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Abstract. While selfish routing has been studied extensively, the problem of designing better coordination mechanisms for routing over time in general graphs has remained an open problem. In this paper, we focus on tree networks (single source multiple destinations) with the goal of minimizing (weighted) average sojourn time of jobs, and provide the first coordination mechanisms with provable price of anarchy for this problem. Interestingly, we achieve our price of anarchy results using simple and strongly local policies such as Shortest Job First and the Smith's Rule (also called HDF). In particular, for the case of unweighted jobs, we design a coordination mechanism with polylogarithmic price of anarchy. For weighted jobs, on the other hand, we show that price of anarchy is a function of the depth of the tree and accompany this result by a lower bound for the price of anarchy for the Smith Rule policy and other common strongly local scheduling policies. Our price of anarchy results also imply improved approximation algorithms for the underlying optimization problem of routing over a tree. This problem is well motivated from applications of routing in supercomputers and data center networks where average sojourn time is an important metric.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Coordination Mechanisms for Selfish Routing over Time on a Tree

Bhattacharya

Kulkarni

Mirrokni

2014

Automata, Languages, and Programming

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“…The designer has to decide in advance local scheduling policies or increases in edge latencies, without knowing the exact input, and has been used for scheduling problems [24,39,42,8,18,26,12,1,2] as well as for simple routing games [25,13].…”

Section: Example 12 (Generalized Weighted Shapley)mentioning

confidence: 99%

Designing Networks with Good Equilibria under Uncertainty

Christodoulou¹,

Sgouritsa

2015

Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms

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We consider the problem of designing network costsharing protocols with good equilibria under uncertainty. The underlying game is a multicast game in a rooted undirected graph with nonnegative edge costs. A set of k terminal vertices or players need to establish connectivity with the root. The social optimum is the Minimum Steiner Tree.We are interested in situations where the designer has incomplete information about the input. We propose two different models, the adversarial and the stochastic. In both models, the designer has prior knowledge of the underlying metric but the requested subset of the players is not known and is activated either in an adversarial manner (adversarial model) or is drawn from a known probability distribution (stochastic model).In the adversarial model, the goal of the designer is to choose a single, universal cost-sharing protocol that has low Price of Anarchy (PoA) for all possible requested subsets of players. The main question we address is: to what extent can prior knowledge of the underlying metric help in the design?We first demonstrate that there exist classes of graphs where knowledge of the underlying metric can dramatically improve the performance of good network cost-sharing design. For outerplanar graph metrics, we provide a universal cost-sharing protocol with constant PoA, in contrast to protocols that, by ignoring the graph metric, cannot achieve PoA better than Ω(log k). Then, in our main technical result, we show that there exist graph metrics, for which knowing the underlying metric does not help and any universal protocol has PoA of Ω(log k), which is tight. We attack this problem by developing new techniques that employ powerful tools from extremal combinatorics, and more specifically Ramsey Theory in high dimensional hypercubes.Then we switch to the stochastic model, where each player is independently activated according to some probability distribution that is known to the * Department of Computer Science, University of Liverpool, UK. Email:gchristo@liverpool.ac.uk. This work was supported by EP/M008118/1, EP/K01000X/1 and LT140046.† Department of Computer Science, University of Liverpool, UK. Email:salkmini@liverpool.ac.uk designer. We show that there exists a randomized ordered protocol that achieves constant PoA. By using standard derandomization techniques, we produce a deterministic ordered protocol that achieves constant PoA. We remark, that the first result holds also for the black-box model, where the probabilities are not known to the designer, but is allowed to draw independent (polynomially many) samples.

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“…The concept of universal solutions has also been used in other contexts, notably in the context of hash functions [5] and routing [32]. Finally, there is also some connection with the notion of coordination mechanisms [6], where the task is to design algorithms with good equilibrium solutions, and also with the design of universal ordered protocols which is discussed in [7].…”

Section: Introductionmentioning

confidence: 99%

An Improved Upper Bound for the Universal TSP on the Grid

Christodoulou¹,

Sgouritsa²

2017

Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms

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We study the universal Traveling Salesman Problem in an n × n grid with the shortest path metric. The goal is to define a (universal) total ordering over the set of grid's vertices, in a way that for any input (subset of vertices), the tour, which visits the points in this ordering, is a good approximation of the optimal tour, i.e. has low competitive ratio.This problem was first studied by Platzman and Bartholdi [26]. They proposed a heuristic, which was based on the Sierpinski space-filling curve, in order to define a universal ordering of the unit square [0, 1] 2 under the Euclidean metric. Their heuristic visits the points of the unit square in the order of their appearance along the space-filling curve. They provided a logarithmic upper bound which was shown to be tight up to a constant by Bertsimas and Grigni [3]. Bertsimas and Grigni further showed logarithmic lower bounds for other space-filling curves and they conjectured that any universal ordering has a logarithmic lower bound for the n × n grid.In this work, we disprove this conjecture by showing that there exists a universal ordering of the n × n grid with competitive ratio of O log n log log n . The heuristic we propose defines a universal ordering of the grid's vertices based on a generalization of the Lebesgue spacefilling curve. In order to analyze the competitive ratio of our heuristic, we employ techniques from the theory of geometric spanners in Euclidean spaces. We finally show that our analysis is tight up to a constant.

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Coordination mechanisms

Cited by 119 publications

References 39 publications

Coordination Mechanisms for Selfish Routing over Time on a Tree

Coordination Mechanisms for Selfish Routing over Time on a Tree

Designing Networks with Good Equilibria under Uncertainty

An Improved Upper Bound for the Universal TSP on the Grid

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