Minimum-energy broadcast in random-grid ad-hoc networks: approximation and distributed algorithms

The Min Energy broadcast problem consists in assigning transmission ranges to the nodes of an ad-hoc network in order to guarantee a directed spanning tree from a given source node and, at the same time, to minimize the energy consumption (i.e. the energy cost) yielded by the range assignment. Min energy broadcast is known to be NP-hard. We consider random-grid networks where nodes are chosen independently at random from the $n$ points of a $\sqrt n \times \sqrt n$ square grid in the plane. The probability of the existence of a node at a given point of the grid does depend on that point, that is, the probability distribution can be non-uniform. By using information-theoretic arguments, we prove a lower bound $(1-\epsilon) \frac n{\pi}$ on the energy cost of any feasible solution for this problem. Then, we provide an efficient solution of energy cost not larger than $1.1204 \frac n{\pi}$. Finally, we present a fully-distributed protocol that constructs a broadcast range assignment of energy cost not larger than $8n$,thus still yielding constant approximation. The energy load is well balanced and, at the same time, the work complexity (i.e. the energy due to all message transmissions of the protocol) is asymptotically optimal. The completion time of the protocol is only an $O(\log n)$ factor slower than the optimum. The approximation quality of our distributed solution is also experimentally evaluated. All bounds hold with probability at least $1-1/n^{\Theta(1)}$.Comment: 13 pages, 3 figures, 1 tabl

On the average case performance of some greedy approximation algorithms for the uncapacitated facility location problem

In combinatorial optimization, a popular approach to NP-hard problems is the design of approximation algorithms. These algorithms typically run in polynomial time and are guaranteed to produce a solution which is within a known multiplicative factor of optimal. Unfortunately, the known factor is often known to be large in pathological instances. Conventional wisdom holds that, in practice, approximation algorithms will produce solutions closer to optimal than their proven guarantees. In this paper, we use the rigorous-analysis-of-heuristics framework to investigate this conventional wisdom. We analyze the performance of 3 related approximation algorithms for the uncapacitated facility location problem (from [Jain, Mahdian, Markakis, Saberi, Vazirani, 2003] and [Mahdian, Ye, Zhang, 2002]) when each is applied to an instances created by placing n points uniformly at random in the unit square. We find that, with high probability, these 3 algorithms do not find asymptotically optimal solutions, and, also with high probability, a simple plane partitioning heuristic does find an asymptotically optimal solution

On the average case performance of some greedy approximation algorithms for the uncapacitated facility location problem

In combinatorial optimization, a popular approach to NPhard problems is the design of approximation algorithms. These algorithms typically run in polynomial time and are guaranteed to produce a solution which is within a known multiplicative factor of optimal. Unfortunately, the known factor is often known to be large in pathological instances. Conventional wisdom holds that, in practice, approximation algorithms will produce solutions closer to optimal than their proven guarantees. In this paper, we use the rigorousanalysis-of-heuristics framework to investigate this conventional wisdom. We analyze the performance of 3 related approximation algorithms for the uncapacitated facility location problem (from [Jain, Mahdian, Markakis, Saberi, Vazirani, 2003] and [Mahdian, Ye, Zhang, 2002]) when each is applied to an instances created by placing n points uniformly at random in the unit square. We find that, with high probability, these 3 algorithms do not find asymptotically optimal solutions, and, also with high probability, a simple plane partitioning heuristic does find an asymptotically optimal solution. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]

Resolution Search et problèmes d'optimisation discrète

Les problèmes d optimisation discrète sont pour beaucoup difficiles à résoudre, depar leur nature combinatoire. Citons par exemple les problèmes de programmationlinéaire en nombres entiers. Une approche couramment employée pour les résoudreexactement est l approche de Séparation et Évaluation Progressive. Une approchedifférente appelée Resolution Search a été proposée par Chvátal en 1997 pourrésoudre exactement des problèmes d optimisation à variables 0-1, mais elle restemal connue et n a été que peu appliquée depuis.Cette thèse tente de remédier à cela, avec un succès partiel. Une première contributionconsiste en la généralisation de Resolution Search à tout problème d optimisationdiscrète, tout en introduisant de nouveaux concepts et définitions. Ensuite,afin de confirmer l intérêt de cette approche, nous avons essayé de l appliquer enpratique pour résoudre efficacement des problèmes bien connus. Bien que notrerecherche n ait pas abouti sur ce point, elle nous a amené à de nouvelles méthodespour résoudre exactement les problèmes d affectation généralisée et de localisationsimple. Après avoir présenté ces méthodes, la thèse conclut avec un bilan et desperspectives sur l application pratique de Resolution Search.The combinatorial nature of discrete optimization problems often makes them difficultto solve. Consider for instance integer linear programming problems, which arecommonly solved using a Branch-and-Bound approach. An alternative approach,Resolution Search, was proposed by Chvátal in 1997 for solving 0-1 optimizationproblems, but remains little known to this day and as such has seen few practicalapplications.This thesis attempts to remedy this state of affairs, with partial success. Itsfirst contribution consists in the generalization of Resolution Search to any discreteoptimization problem, while introducing new definitions and concepts. Next, wetried to validate this approach by attempting to solve well-known problems efficientlywith it. Although our research did not succeed in this respect, it lead usto new methods for solving the generalized assignment and uncapacitated facilitylocation problems. After presenting these methods, this thesis concludes with asummary of our attempts at practical application of Resolution Search, along withfurther perspectives on this matter.AVIGNON-Bib. numérique (840079901) / SudocSudocFranceF

Building efficient wireless infrastructures for pervasive computing environments

Pervasive computing is an emerging concept that thoroughly brings computing devices and the consequent technology into people\u27s daily life and activities. Most of these computing devices are very small, sometimes even invisible , and often embedded into the objects surrounding people. In addition, these devices usually are not isolated, but networked with each other through wireless channels so that people can easily control and access them. In the architecture of pervasive computing systems, these small and networked computing devices form a wireless infrastructure layer to support various functionalities in the upper application layer.;In practical applications, the wireless infrastructure often plays a role of data provider in a query/reply model, i.e., applications issue a query requesting certain data and the underlying wireless infrastructure is responsible for replying to the query. This dissertation has focused on the most critical issue of efficiency in designing such a wireless infrastructure. In particular, our problem resides in two domains depending on different definitions of efficiency. The first definition is time efficiency, i.e., how quickly a query can be replied. Many applications, especially real-time applications, require prompt response to a query as the consequent operations may be affected by the prior delay. The second definition is energy efficiency which is extremely important for the pervasive computing devices powered by batteries. Above all, our design goal is to reply to a query from applications quickly and with low energy cost.;This dissertation has investigated two representative wireless infrastructures, sensor networks and RFID systems, both of which can serve applications with useful information about the environments. We have comprehensively explored various important and representative problems from both algorithmic and experimental perspectives including efficient network architecture design and efficient protocols for basic queries and complicated data mining queries. The major design challenges of achieving efficiency are the massive amount of data involved in a query and the extremely limited resources and capability each small device possesses. We have proposed novel and efficient solutions with intensive evaluation. Compared to the prior work, this dissertation has identified a few important new problems and the proposed solutions significantly improve the performance in terms of time efficiency and energy efficiency. Our work also provides referrable insights and appropriate methodology to other similar problems in the research community