Implications of Selfish Neighbor Selection in Overlay Networks

In a typical overlay network for routing or content sharing, each node must select a fixed number of immediate overlay neighbors for routing traffic or content queries. A selfish node entering such a network would select neighbors so as to minimize the weighted sum of expected access costs to all its destinations. Previous work on selfish neighbor selection has built intuition with simple models where edges are undirected, access costs are modeled by hop-counts, and nodes have potentially unbounded degrees. However, in practice, important constraints not captured by these models lead to richer games with substantively and fundamentally different outcomes. Our work models neighbor selection as a game involving directed links, constraints on the number of allowed neighbors, and costs reflecting both network latency and node preference. We express a node's "best response" wiring strategy as a k-median problem on asymmetric distance, and use this formulation to obtain pure Nash equilibria. We experimentally examine the properties of such stable wirings on synthetic topologies, as well as on real topologies and maps constructed from PlanetLab and AS-level Internet measurements. Our results indicate that selfish nodes can reap substantial performance benefits when connecting to overlay networks composed of non-selfish nodes. On the other hand, in overlays that are dominated by selfish nodes, the resulting stable wirings are optimized to such great extent that even non-selfish newcomers can extract near-optimal performance through naive wiring strategies.Marie Curie Outgoing International Fellowship of the EU (MOIF-CT-2005-007230); National Science Foundation (CNS Cybertrust 0524477, CNS NeTS 0520166, CNS ITR 0205294, EIA RI 020206

Labeling Schemes for Bounded Degree Graphs

We investigate adjacency labeling schemes for graphs of bounded degree $\Delta = O(1)$. In particular, we present an optimal (up to an additive constant) $\log n + O(1)$ adjacency labeling scheme for bounded degree trees. The latter scheme is derived from a labeling scheme for bounded degree outerplanar graphs. Our results complement a similar bound recently obtained for bounded depth trees [Fraigniaud and Korman, SODA 10], and may provide new insights for closing the long standing gap for adjacency in trees [Alstrup and Rauhe, FOCS 02]. We also provide improved labeling schemes for bounded degree planar graphs. Finally, we use combinatorial number systems and present an improved adjacency labeling schemes for graphs of bounded degree $\Delta$ with $(e+1)\sqrt{n} < \Delta \leq n/5$

EGOIST: Overlay Routing Using Selfish Neighbor Selection

A foundational issue underlying many overlay network applications ranging from routing to P2P file sharing is that of connectivity management, 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 specific applications designed to work well in real deployments, and providing abstractions for the underlying problem that are analytically tractable, especially via game-theoretic analysis. In this paper, we unify these two thrusts by using insights gleaned from novel, realistic theoretic models in the design of Egoist – a prototype overlay routing system that we implemented, deployed, and evaluated on PlanetLab. Using measurements on PlanetLab and trace-based simulations, we demonstrate that Egoist's neighbor selection primitives significantly outperform existing heuristics on a variety of performance metrics, including delay, available bandwidth, and node utilization. Moreover, we demonstrate that Egoist is competitive with an optimal, but unscalable full-mesh approach, remains highly effective under significant churn, is robust to cheating, and incurs minimal overhead. Finally, we discuss some of the potential benefits Egoist may offer to applications.National Science Foundation (CISE/CSR 0720604, ENG/EFRI 0735974, CISE/CNS 0524477, CNS/NeTS 0520166, CNS/ITR 0205294; CISE/EIA RI 0202067; CAREER 04446522); European Commission (RIDS-011923