André Luís Vignatti

Convergence Time to Nash Equilibrium in Selfish Bin Packing

Abstract We consider a game-theoretic bin packing problem and we study the convergence time to a Nash equilibrium. We show that, if the best-response strategy is used, then the number of steps needed to reach Nash equilibrium is O ( m w max 2 + n w max ) and O ( n k w max ) , where n, m, k and w max denotes, resp., the number of items, the number of bins, the number of distinct item sizes, and the size of a largest item.

BOUNDS ON THE CONVERGENCE TIME OF DISTRIBUTED SELFISH BIN PACKING

We consider a game-theoretic bin packing problem with identical items, and we study the convergence time to a Nash equilibrium. In the model proposed, users choose their strategy simultaneously. We deal with two bins and multiple bins cases. We consider the case when users know the load of all bins and cases with less information. We consider two approaches, depending if the system can undo movements that lead to infeasible states. Let n and m be, respectively, the number of items and bins. In the two bins case, we show an O(log log n) and an O(n) bounds when undo movements are allowed and when they are not allowed, resp. In multiple bins case, we show an O(log n) and an O(nm) bounds when undo movements are allowed and when they are not allowed, resp. In the case with less information, we show an O(m log n) and an O(n3m) bounds when undo movements are allowed and when they are not allowed, resp. Also, in the case with less information where the information about completely filled/empty bins is not available, we show an O(m2log n) and an O(n3m3) bounds when undo movements are allowed and when they are not allowed, resp.

Extending OAI-PMH over structured P2P networks for digital preservation

Open archives initiative (OAI) allows both libraries and museums create and share their own low-cost digital libraries (DL). OAI DL are based on OAI-PMH protocol which, although is consolidated as a pattern for disseminating metadata, does not rely on either digital preservation and availability of content, essential requirements in this type of system. Building new mechanisms that guarantee improvements, at no or low cost increases, becomes a great challenge. This article proposes a distributed archiving system based on a P2P network, that allows OAI-based libraries to replicate digital objects to ensure their reliability and availability. The proposed system keeps and extends the current OAI-PMH protocol characteristics and is designed as a set of OAI repositories, where each repository has an independent fail probability assigned to it. Items are inserted with a reliability that is satisfied by replicating them in subsets of repositories. Communication between the nodes (repositories) of the network is organized in a distributed hash table and multiple hash functions are used to select repositories that keep the replicas of each stored item. The OAI characteristics combined with a structured P2P digital preservation system allow the construction of a reliable and totally distributed digital library. The archiving system has been evaluated through experiments in a real environment and the OAI-PMH extension validated by the implementation of a proof-of-principle prototype.

An Approximation Algorithm for the p-Hub Median Problem

Abstract In the p-hub median problem we are given a set of clients V, a set of demands D ⊆ V × V , a cost function ρ : V × V → R + , and an integer p > 0 . The objective is to select terminals T ⊆ V , where | T | ≤ p , and assign each demand to a terminal, in order to minimize the total cost between demands and terminals. We present the first approximation bounds for the problem: a 1 + 2 / e lower bound if NP ⊂ DTIME ( n O ( log ⁡ log ⁡ n ) ) , and a (4α)-approximation algorithm if we are allowed to open at most ( 2 α 2 α − 1 ) p terminals, where α > 1 is a trade off parameter.

Long-term digital archiving based on selection of repositories over P2P networks

The importance of digital information is constantly increasing in the last years. Such information often needs to be preserved for a long-term and this is the responsibility of digital archiving systems. This paper proposes a reliable replication model of immutable digital content to be used in long-term archiving systems. The archiving system is modeled as a set of storage repositories where each repository has an independent fail probability assigned to it. Items are inserted with a reliability that is satisfied by replicating them in subsets of repositories. Through simulation, we evaluated three different proposed strategies to create replicas. It is also proposed a completely distributed archiving system using this model over a structured peer-to-peer (P2P) network. The communication between the nodes (repositories) of the network is organized in a distributed hash table and multiple hash functions are used to select repositories that will keep the replicas of each stored item. The system is evaluated through experiments in a real environment. The proposed model and the algorithms, combined with the structured P2P scalability made possible the construction of a reliable and totally distributed digital archiving system.

Distributed selfish bin packing

We consider a game-theoretic bin packing problem with identical items, and we study the convergence time to a Nash equilibrium. In the model proposed, users choose their strategy simultaneously. We deal with two bins and multiple bins cases. We consider the case when users know the load of all bins and a case with less information. We consider two approaches, depending if the system can undo movements that lead to infeasible states. In the two bins case, we show an O(log log n) bound when undo movements are allowed. In multiple bins case, we show an O(log n) and an O(nm) bounds when undo movements are allowed and when they are not allowed, resp. In the case with less information, we show an O(mlog n) and an O(n3m) bounds when undo movements are allowed and when they are not allowed, resp.

A preselection algorithm for the influence maximization problem in power law graphs

The influence maximization problem in social networks seeks out a set of nodes that allows spreading information to the greatest number of members. A greedy algorithm, proposed by Kempe et al. [12], finds a solution in which the spread of influence is at least 1 - 1/e of the optimum. However, some shortcomings of this approach negatively affect the run time of this algorithm. In this work, we propose a methodology to speedup the Kempes algorithm with focus on power law graphs. The improvement consists of choosing the most promising nodes in advance. To this end, we explore some properties of power law graphs and the relationship between social influence and degree distribution. We have verified by experimental analysis that this preselection reduces the run time while preserving the quality of the solution.

Minimum vertex cover in generalized random graphs with power law degree distribution

In this paper we study the approximability of the minimum vertex cover problem in power law graphs. In particular, we investigate the behavior of a standard 2-approximation algorithm together with a simple pre-processing step when the input is a random sample from a generalized random graph model with power law degree distribution. More precisely, if the probability of a vertex of degree i to be present in the graph is c i - β , where β 2 and c is a normalizing constant, the expected approximation ratio is 1 + ź ( β ) - 1 L i β ( e - ź ( β ) ) , where ź ( β ) is the Riemann Zeta function of β, Li ( β ) is the polylogarithmic special function of β and ź ( β ) = Li β - 2 ( 1 e ) ź ( β - 1 ) .