Abstract: We argue the case for a new paradigm for architecting structured P2P overlay networks, coined AESOP. AESOP consists of 3 layers: (i) an architecture, PLANES, that ensures significant performance speedups, assuming knowledge of altruistic peers; (ii) an accounting/auditing layer, AltSeAl, that identifies and validates altruistic peers; and (iii) SeAledPLANES, a layer that facilitates the coordination/collaboration of the previous two components. We briefly present these components along with experimental and analytical data of the promised significant performance gains and the related overhead. In light of these very encouraging results, we put this three-layer architecture paradigm forth as the way to structure the P2P overlay networks of the future.

Abstract: We investigate the problem of efficient data collection in wireless sensor networks where both the sensors and the sink move. We especially study the important, realistic case where the spatial distribution of sensors is non-uniform and their mobility is diverse and dynamic. The basic idea of our protocol is for the sink to benefit of the local information that sensors spread in the network as they move, in order to extract current local conditions and accordingly adjust its trajectory. Thus, sensory motion anyway present in the network serves as a low cost replacement of network information propagation. In particular, we investigate two variations of our method: a) the greedy motion of the sink towards the region of highest density each time and b) taking into account the aggregate density in wider network regions. An extensive comparative evaluation to relevant data collection methods (both randomized and optimized deterministic), demonstrates that our approach achieves significant performance gains, especially in non-uniform placements (but also in uniform ones). In fact, the greedy version of our approach is more suitable in networks where the concentration regions appear in a spatially balanced manner, while the aggregate scheme is more appropriate in networks where the concentration areas are geographically correlated. We also investigate the case of multiple sinks by suggesting appropriate distributed coordination methods.

Abstract: We consider selfish routing over a network consisting of m parallellinks through which $n$ selfish users route their traffic trying tominimize their own expected latency. We study the class of mixedstrategies in which the expected latency through each link is at mosta constant multiple of the optimum maximum latency had globalregulation been available. For the case of uniform links it is knownthat all Nash equilibria belong to this class of strategies. We areinterested in bounding the coordinationratio (or price of anarchy) ofthese strategies defined as the worst-case ratio of the maximum (overall links) expected latency over the optimum maximum latency. The loadbalancing aspect of the problem immediately implies a lower boundO(ln m ln ln m) of the coordinationratio. We give a tight (up to a multiplicative constant) upper bound.To show the upper bound, we analyze a variant of the classical ballsand bins problem, in which balls with arbitrary weights are placedinto bins according to arbitrary probability distributions. At theheart of our approach is a new probabilistic tool that we call ballfusion; this tool is used to reduce the variant of the problem whereballs bear weights to the classical version (with no weights). Ballfusion applies to more general settings such as links with arbitrarycapacities and other latency functions.

Abstract: We present three new coordination mechanisms for schedul-
ing n sel¯sh jobs on m unrelated machines. A coordination
mechanism aims to mitigate the impact of sel¯shness of jobs
on the e±ciency of schedules by de¯ning a local schedul-
ing policy on each machine. The scheduling policies induce
a game among the jobs and each job prefers to be sched-
uled on a machine so that its completion time is minimum
given the assignments of the other jobs. We consider the
maximum completion time among all jobs as the measure
of the e±ciency of schedules. The approximation ratio of
a coordination mechanism quanti¯es the e±ciency of pure
Nash equilibria (price of anarchy) of the induced game. Our
mechanisms are deterministic, local, and preemptive in the
sense that the scheduling policy does not necessarily process
the jobs in an uninterrupted way and may introduce some
idle time. Our ¯rst coordination mechanism has approxima-
tion ratio O(logm) and always guarantees that the induced
game has pure Nash equilibria to which the system con-
verges in at most n rounds. This result improves a recent
bound of O(log2 m) due to Azar, Jain, and Mirrokni and,
similarly to their mechanism, our mechanism uses a global
ordering of the jobs according to their distinct IDs. Next
we study the intriguing scenario where jobs are anonymous,
i.e., they have no IDs. In this case, coordination mechanisms
can only distinguish between jobs that have diffeerent load
characteristics. Our second mechanism handles anonymous
jobs and has approximation ratio O
¡ logm
log logm
¢
although the
game induced is not a potential game and, hence, the exis-
tence of pure Nash equilibria is not guaranteed by potential
function arguments. However, it provides evidence that the
known lower bounds for non-preemptive coordination mech-
anisms could be beaten using preemptive scheduling poli-
cies. Our third coordination mechanism also handles anony-
mous jobs and has a nice \cost-revealing" potential func-
tion. Besides in proving the existence of equilibria, we use
this potential function in order to upper-bound the price of stability of the induced game by O(logm), the price of an-
archy by O(log2 m), and the convergence time to O(log2 m)-
approximate assignments by a polynomial number of best-
response moves. Our third coordination mechanism is the
¯rst that handles anonymous jobs and simultaneously guar-
antees that the induced game is a potential game and has
bounded price of anarchy.

Abstract: In large scale networks users often behave selfishly trying to minimize their routing cost. Modelling this as a noncooperative game, may yield a Nash equilibrium with unboundedly poor network performance. To measure this inefficacy, the CoordinationRatio or Price of Anarchy (PoA) was introduced. It equals the ratio of the cost induced by the worst Nash equilibrium, to the corresponding one induced by the overall optimum assignment of the jobs to the network. On improving the PoA of a given network, a series of papers model this selfish behavior as a Stackelberg or Leader-Followers game.
We consider random tuples of machines, with either linear or M/M/1 latency functions, and PoA at least a tuning parameter c. We validate a variant (NLS) of the Largest Latency First (LLF) Leaderrsquos strategy on tuples with PoA ge c. NLS experimentally improves on LLF for systems with inherently high PoA, where the Leader is constrained to control low portion agr of jobs. This suggests even better performance for systems with arbitrary PoA. Also, we bounded experimentally the least Leaderrsquos portion agr0 needed to induce optimum cost. Unexpectedly, as parameter c increases the corresponding agr0 decreases, for M/M/1 latency functions. All these are implemented in an extensive Matlab toolbox.

Abstract: Let M be a single s-t network of parallel links with load dependent latency functions shared by an infinite number of selfish users. This may yield a Nash equilibrium with unbounded CoordinationRatio [E. Koutsoupias, C. Papadimitriou, Worst-case equilibria, in: 16th Annual Symposium on Theoretical Aspects of Computer Science, STACS, vol. 1563, 1999, pp. 404-413; T. Roughgarden, E. Tardos, How bad is selfish routing? in: 41st IEEE Annual Symposium of Foundations of Computer Science, FOCS, 2000, pp. 93-102]. A Leader can decrease the coordinationratio by assigning flow {\'a}r on M, and then all Followers assign selfishly the (1-{\'a})r remaining flow. This is a Stackelberg Scheduling Instance(M,r,{\'a}),0≤{\'a}≤1. It was shown [T. Roughgarden, Stackelberg scheduling strategies, in: 33rd Annual Symposium on Theory of Computing, STOC, 2001, pp. 104-113] that it is weakly NP-hard to compute the optimal Leader's strategy. For any such network M we efficiently compute the minimum portion @b"M of flow r>0 needed by a Leader to induce M's optimum cost, as well as her optimal strategy. This shows that the optimal Leader's strategy on instances (M,r,@a>=@b"M) is in P. Unfortunately, Stackelberg routing in more general nets can be arbitrarily hard. Roughgarden presented a modification of Braess's Paradox graph, such that no strategy controlling {\'a}r flow can induce ≤1/{\'a} times the optimum cost. However, we show that our main result also applies to any s-t net G. We take care of the Braess's graph explicitly, as a convincing example. Finally, we extend this result to k commodities. A conference version of this paper has appeared in [A. Kaporis, P. Spirakis, The price of optimum in stackelberg games on arbitrary single commodity networks and latency functions, in: 18th annual ACM symposium on Parallelism in Algorithms and Architectures, SPAA, 2006, pp. 19-28]. Some preliminary results have also appeared as technical report in [A.C. Kaporis, E. Politopoulou, P.G. Spirakis, The price of optimum in stackelberg games, in: Electronic Colloquium on Computational Complexity, ECCC, (056), 2005].

Abstract: We study the problem of routing traffic through a congested network. We focus on the simplest case of a network consisting of m parallel links. We assume a collection of n network users; each user employs a mixed strategy, which is a probability distribution over links, to control the shipping of its own assigned traffic. Given a capacity for each link specifying the rate at which the link processes traffic, the objective is to route traffic so that the maximum (over all links) latency is minimized. We consider both uniform and arbitrary link capacities. How much decrease in global performace is necessary due to the absence of some central authority to regulate network traffic and implement an optimal assignment of traffic to links? We investigate this fundamental question in the context of Nash equilibria for such a system, where each network user selfishly routes its traffic only on those links available to it that minimize its expected latency cost, given the network congestion caused by the other users. We use the CoordinationRatio, originally defined by Koutsoupias and Papadimitriou, as a measure of the cost of lack of coordination among the users; roughly speaking, the CoordinationRatio is the ratio of the expectation of the maximum (over all links) latency in the worst possible Nash equilibrium, over the least possible maximum latency had global regulation been available. Our chief instrument is a set of combinatorial Minimum Expected Latency Cost Equations, one per user, that characterize the Nash equilibria of this system. These are linear equations in the minimum expected latency costs, involving the user traffics, the link capacities, and the routing pattern determined by the mixed strategies. In turn, we solve these equations in the case of fully mixed strategies, where each user assigns its traffic with a strictly positive probability to every link, to derive the first existence and uniqueness results for fully mixed Nash equilibria in this setting. Through a thorough analysis and characterization of fully mixed Nash equilibria, we obtain tight upper bounds of no worse than O(ln n/ln ln n) on the CoordinationRatio for (i) the case of uniform capacities and arbitrary traffics and (ii) the case of arbitrary capacities and identical traffics.