Showing papers by "John Augustine published in 2011"

Dynamics of profit-sharing games

Abstract: An important task in the analysis of multiagent systems is to understand how groups of selfish players can form coalitions, i.e., work together in teams. In this paper, we study the dynamics of coalition formation under bounded rationality. We consider settings where each team's profit is given by a concave function, and propose three profit-sharing schemes, each of which is based on the concept of marginal utility. The agents are assumed to be myopic, i.e., they keep changing teams as long as they can increase their payoff by doing so. We study the properties (such as closeness to Nash equilibrium or total profit) of the states that result after a polynomial number of such moves, and prove bounds on the price of anarchy and the price of stability of the corresponding games.

Distributed Agreement in Dynamic Peer-to-Peer Networks

Abstract: Motivated by the need for robust and fast distributed computation in highly dynamic Peer-to-Peer (P2P) networks, we study algorithms for the fundamental distributed agreement problem. P2P networks are highly dynamic networks that experience heavy node {\em churn}. Our goal is to design fast algorithms (running in a small number of rounds) that guarantee, despite high node churn rate, that almost all nodes reach a stable agreement. Our main contributions are randomized distributed algorithms that guarantee {\em stable almost-everywhere agreement} with high probability even under high adversarial churn in a polylogarithmic number of rounds: 1. An $O(\log^2 n)$-round ($n$ is the stable network size) randomized algorithm that achieves almost-everywhere agreement with high probability under up to {\em linear} churn {\em per round} (i.e., $\epsilon n$, for some small constant $\epsilon > 0$), assuming that the churn is controlled by an oblivious adversary (that has complete knowledge and control of what nodes join and leave and at what time and has unlimited computational power, but is oblivious to the random choices made by the algorithm). Our algorithm requires only polylogarithmic in $n$ bits to be processed and sent (per round) by each node. 2. An $O(\log m\log^3 n)$-round randomized algorithm that achieves almost-everywhere agreement with high probability under up to $\epsilon \sqrt{n}$ churn per round (for some small $\epsilon > 0$), where $m$ is the size of the input value domain, that works even under an adaptive adversary (that also knows the past random choices made by the algorithm). This algorithm requires up to polynomial in $n$ bits (and up to $O(\log m)$ bits) to be processed and sent (per round) by each node.

Enforcing efficient equilibria in network design games via subsidies

Abstract: The efficient design of networks has been an important engineering task that involves challenging combinatorial optimization problems. Typically, a network designer has to select among several alternatives which links to establish so that the resulting network satisfies a given set of connectivity requirements and the cost of establishing the network links is as low as possible. The Minimum Spanning Tree problem, which is well-understood, is a nice example. In this paper, we consider the natural scenario in which the connectivity requirements are posed by selfish users who have agreed to share the cost of the network to be established according to a well-defined rule. The design proposed by the network designer should now be consistent not only with the connectivity requirements but also with the selfishness of the users. Essentially, the users are players in a so-called network design game and the network designer has to propose a design that is an equilibrium for this game. As it is usually the case when selfishness comes into play, such equilibria may be suboptimal. In this paper, we consider the following question: can the network designer enforce particular designs as equilibria or guarantee that efficient designs are consistent with users' selfishness by appropriately subsidizing some of the network links? In an attempt to understand this question, we formulate corresponding optimization problems and present positive and negative results.

Localized Geometric Query Problems

Abstract: A new class of geometric query problems are studied in this paper. We are required to preprocess a set of geometric objects $P$ in the plane, so that for any arbitrary query point $q$, the largest circle that contains $q$ but does not contain any member of $P$, can be reported efficiently. The geometric sets that we consider are point sets and boundaries of simple polygons.

Tight analysis of shortest path convergecast in wireless sensor networks

Abstract: We consider the convergecast problem in wireless sensor networks where readings generated by each sensor node are to reach the sink. Since a sensor reading can usually be encoded in a few bytes, more than one reading can readily fit into a standard transmission packet. We assume that any such packet consumes one unit of energy every time it hops from a node to a neighbor regardless of the total size of the readings in it. Our objective is to minimize the total energy consumed to send all the readings to the sink. Consequently, we ask the question: can we pack the readings in common routes to minimize the number of hops? It is quite elementary to see that this problem is NP-hard when the size of the readings are arbitrary via reductions from bin packing or set partition. We study the simple version with readings normalized to 1 byte in length. However, we make no assumptions on the underlying graph. We show this to be NP-hard by way of a reduction from Set Cover. We study a class SPEP of distributed algorithms that is completely defined by two properties. Firstly, the packets hop along some shortest path to the sink. Secondly, given all the readings that enter into a node, it sends out as many fully packed packets as possible followed by at most one partial packet --- the elementary packing property. We show that any algorithm in this class is (2−3/2k)-approximate where k ≥ 2 is the size of a data packet in bytes. We additionally show that this class is optimal when the underlying sensor network is a tree or grid topology. Our main technical contribution is a lower bound. We show that no algorithm that either follows the shortest path or packs in an elementary manner is a (2 − e)-approximation, for any fixed e > 0.