Reducibility among Fractional Stability Problems

Kintali, Shiva; Poplawski, Laura J.; Rajaraman, Rajmohan; Sundaram, Ravi; Teng, Shang‐Hua

doi:10.1137/120874655

Cited by 24 publications

(15 citation statements)

References 25 publications

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“…Only recently Laoutaris et. al [39] studied the fractional bounded budget connection games and Kintali et al [51] studied the complexity of Nash equilibria in such games.…”

Section: Related Workmentioning

confidence: 99%

Selfish Overlay Network Creation and Maintenance

Smaragdakis

Laoutaris

Lekakis

et al. 2011

IEEE/ACM Trans. Networking

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Abstract-A foundational issue underlying many overlay network applications ranging from routing to peer-to-peer file sharing is that of the network formation, i.e., folding new arrivals into an existing overlay, and re-wiring to cope with changing network conditions. Previous work has considered the problem from two perspectives: devising practical heuristics for the case of cooperative peers, and performing game theoretic analysis for the case of selfish peers. In our work, we unify the aforementioned thrusts by defining and studying the Selfish Neighbor Selection (SNS) game and its application to overlay routing. At the heart of SNS stands the restriction that peers are allowed up to a certain number of neighbors. This makes SNS substantially different from existing network formation games that impose no bounds on peer degrees. Having bounded degrees has important practical consequences as it permits the creation of overlay structures that require O(n) instead of O(n 2 ) link monitoring overhead. We show that a node's "best response" wiring strategy amounts to solving a k-median problem on asymmetric distance. Best response wirings have substantial practical utility as they permit selfish nodes to reap substantial performance benefits when connecting to overlays of non-selfish nodes. A more intricate consequence is that even non-selfish nodes can benefit from the existence of some selfish nodes since the latter, via their local optimizations, create a highly optimized backbone, upon which even simple heuristic wirings yield good performance. To capitalize on the above properties we design, build and deploy, EGOIST, an SNS-inspired prototype overlay routing system for PlanetLab. We demonstrate that EGOIST outperforms existing heuristic overlays on a variety of performance metrics, including delay, available bandwidth, and node utilization, while it remains competitive with an optimal, but unscalable full-mesh overlay.

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“…Only recently Laoutaris et. al [39] studied the fractional bounded budget connection games and Kintali et al [51] studied the complexity of Nash equilibria in such games.…”

Section: Related Workmentioning

confidence: 99%

Selfish Overlay Network Creation and Maintenance

Smaragdakis

Laoutaris

Lekakis

et al. 2011

IEEE/ACM Trans. Networking

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show abstract

“…In the case of PPAD this is the parity argument on a directed graph, equivalent to the existence guarantee of Brouwer fixpoints: a Brouwer function is a continuous function f : D → D where D is a convex compact domain, and Brouwer's fixed point theorem guarantees a point x for which f (x) = x. PPAD has been widely used to classify problems of computing game-theoretic equilibria (a long line of work on Nash equilibrium computation beginning with Daskalakis et al [2009]; Chen et al [2009b] and market equilibria, e.g., Chen et al [2009a]). PPAD also captures diverse problems in combinatorics and cooperative game theory [Kintali et al, 2013].…”

Section: Np Total Search Classes: Ppad Pls and Clsmentioning

confidence: 99%

The Complexity of Gradient Descent: CLS = PPAD ∩ PLS

Fearnley

Goldberg

Hollender

et al. 2022

J. ACM

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We study search problems that can be solved by performing Gradient Descent on a bounded convex polytopal domain and show that this class is equal to the intersection of two well-known classes: PPAD and PLS. As our main underlying technical contribution, we show that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain [0, 1] 2 is PPAD ∩ PLS-complete. This is the first non-artificial problem to be shown complete for this class. Our results also imply that the class CLS (Continuous Local Search) – which was defined by Daskalakis and Papadimitriou as a more “natural” counterpart to PPAD ∩ PLS and contains many interesting problems – is itself equal to PPAD ∩ PLS.

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“…Kintali et al [8] showed that finding a stable fractional hypergraph matching is PPAD-complete. We reduce this problem to the stable multicommodity flow problem in order to prove the following theorem.…”

Section: Ppad-hardnessmentioning

confidence: 99%

Stable Multicommodity Flows

Király

Pap

2013

Algorithms

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We extend the stable flow model of Fleiner to multicommodity flows. In addition to the preference lists of agents on trading partners for each commodity, every trading pair has a preference list on the commodities that the seller can sell to the buyer. A blocking walk (with respect to a certain commodity) may include saturated arcs, provided that a positive amount of less preferred commodity is traded along the arc. We prove that a stable multicommodity flow always exists, although it is PPAD-hard to find one.

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Reducibility among Fractional Stability Problems

Cited by 24 publications

References 25 publications

Selfish Overlay Network Creation and Maintenance

Selfish Overlay Network Creation and Maintenance

The Complexity of Gradient Descent: CLS = PPAD ∩ PLS

Stable Multicommodity Flows

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