71 research outputs found
Optimality Clue for Graph Coloring Problem
In this paper, we present a new approach which qualifies or not a solution
found by a heuristic as a potential optimal solution. Our approach is based on
the following observation: for a minimization problem, the number of admissible
solutions decreases with the value of the objective function. For the Graph
Coloring Problem (GCP), we confirm this observation and present a new way to
prove optimality. This proof is based on the counting of the number of
different k-colorings and the number of independent sets of a given graph G.
Exact solutions counting problems are difficult problems (\#P-complete).
However, we show that, using only randomized heuristics, it is possible to
define an estimation of the upper bound of the number of k-colorings. This
estimate has been calibrated on a large benchmark of graph instances for which
the exact number of optimal k-colorings is known. Our approach, called
optimality clue, build a sample of k-colorings of a given graph by running many
times one randomized heuristic on the same graph instance. We use the
evolutionary algorithm HEAD [Moalic et Gondran, 2018], which is one of the most
efficient heuristic for GCP. Optimality clue matches with the standard
definition of optimality on a wide number of instances of DIMACS and RBCII
benchmarks where the optimality is known. Then, we show the clue of optimality
for another set of graph instances. Optimality Metaheuristics Near-optimal
Proof of the satisfiability conjecture for large k
We establish the satisfiability threshold for random -SAT for all , with an absolute constant. That is, there exists a limiting density
such that a random -SAT formula of clause density is
with high probability satisfiable for , and unsatisfiable for
. We show that the threshold is given explicitly
by the one-step replica symmetry breaking prediction from statistical physics.
The proof develops a new analytic method for moment calculations on random
graphs, mapping a high-dimensional optimization problem to a more tractable
problem of analyzing tree recursions. We believe that our method may apply to a
range of random CSPs in the 1-RSB universality class
Swarm intelligence techniques for optimization and management tasks insensor networks
The main contributions of this thesis are located in the domain of wireless sensor netorks. More in detail, we introduce energyaware
algorithms and protocols in the context of the following topics: self-synchronized duty-cycling in networks with energy
harvesting capabilities, distributed graph coloring and minimum energy broadcasting with realistic antennas. In the following, we
review the research conducted in each case.
We propose a self-synchronized duty-cycling mechanism for sensor networks. This mechanism is based on the working and resting
phases of natural ant colonies, which show self-synchronized activity phases. The main goal of duty-cycling methods is to save
energy by efficiently alternating between different states. In the case at hand, we considered two different states: the sleep state,
where communications are not possible and energy consumption is low; and the active state, where communication result in a
higher energy consumption.
In order to test the model, we conducted an extensive experimentation with synchronous simulations on mobile networks and static
networks, and also considering asynchronous networks. Later, we extended this work by assuming a broader point of view and
including a comprehensive study of the parameters. In addition, thanks to a collaboration with the Technical University of
Braunschweig, we were able to test our algorithm in the real sensor network simulator Shawn (http://shawn.sf.net).
The second part of this thesis is devoted to the desynchronization of wireless sensor nodes and its application to the distributed
graph coloring problem. In particular, our research is inspired by the calling behavior of Japanese tree frogs, whose males use their
calls to attract females. Interestingly, as female frogs are only able to correctly localize the male frogs when their calls are not too
close in time, groups of males that are located nearby each other desynchronize their calls.
Based on a model of this behavior from the literature, we propose a novel algorithm with applications to the field of sensor
networks. More in detail, we analyzed the ability of the algorithm to desynchronize neighboring nodes. Furthermore, we considered
extensions of the original model, hereby improving its desynchronization capabilities.To illustrate the potential benefits of
desynchronized networks, we then focused on distributed graph coloring. Later, we analyzed the algorithm more extensively and
show its performance on a larger set of benchmark instances.
The classical minimum energy broadcast (MEB) problem in wireless ad hoc networks, which is well-studied in the scientific
literature, considers an antenna model that allows the adjustment of the transmission power to any desired real value from zero up
to the maximum transmission power level. However, when specifically considering sensor networks, a look at the currently
available hardware shows that this antenna model is not very realistic. In this work we re-formulate the MEB problem for an
antenna model that is realistic for sensor networks. In this antenna model transmission power levels are chosen from a finite set of
possible ones. A further contribution concerns the adaptation of an ant colony optimization algorithm --currently being the state of
the art for the classical MEB problem-- to the more realistic problem version, the so-called minimum energy broadcast problem with
realistic antennas (MEBRA). The obtained results show that the advantage of ant colony optimization over classical heuristics even
grows when the number of possible transmission power levels decreases. Finally we build a distributed version of the algorithm,
which also compares quite favorably against centralized heuristics from the literature.Las principles contribuciones de esta tesis se encuentran en el domino de las redes de sensores inalámbricas. Más en detalle, introducimos algoritmos y protocolos que intentan minimizar el consumo energético para los siguientes problemas: gestión autosincronizada de encendido y apagado de sensores con capacidad para obtener energÃa del ambiente, coloreado de grafos distribuido y broadcasting de consumo mÃnimo en entornos con antenas reales.
En primer lugar, proponemos un sistema capaz de autosincronizar los ciclos de encendido y apagado de los nodos de una red de sensores. El mecanismo está basado en las fases de trabajo y reposo de las colonias de hormigas tal y como estas pueden observarse en la naturaleza, es decir, con fases de actividad autosincronizadas. El principal objectivo de este tipo de técnicas es ahorrar energÃa gracias a alternar estados de forma eficiente. En este caso en concreto, consideramos dos estados diferentes: el estado dormido, en el que los nodos no pueden comunicarse y el consumo energético es bajo; y el estado activo, en el que las comunicaciones propician un consumo energético elevado.
Con el objetivo de probar el modelo, se ha llevado a cabo una extensa experimentación que incluye tanto simulaciones sÃncronas en redes móviles y estáticas, como simulaciones en redes asÃncronas. Además, este trabajo se extendió asumiendo un punto de vista más amplio e incluyendo un detallado estudio de los parámetros del algoritmo. Finalmente, gracias a la colaboración con la Technical University of Braunschweig, tuvimos la oportunidad de probar el mecanismo en el simulador realista de redes de sensores, Shawn (http://shawn.sf.net).
La segunda parte de esta tesis está dedicada a la desincronización de nodos en redes de sensores y a su aplicación al problema del coloreado de grafos de forma distribuida. En particular, nuestra investigación está inspirada por el canto de las ranas de árbol japonesas, cuyos machos utilizan su canto para atraer a las hembras. Resulta interesante que debido a que las hembras solo son capaces de localizar las ranas macho cuando sus cantos no están demasiado cerca en el tiempo, los grupos de machos que se hallan en una misma región desincronizan sus cantos.
Basado en un modelo de este comportamiento que se encuentra en la literatura, proponemos un nuevo algoritmo con aplicaciones al campo de las redes de sensores. Más en detalle, analizamos la habilidad del algoritmo para desincronizar nodos vecinos. Además, consideramos extensiones del modelo original, mejorando su capacidad de desincronización. Para ilustrar los potenciales beneficios de las redes desincronizadas, nos centramos en el problema del coloreado de grafos distribuido que tiene relación con diferentes tareas habituales en redes de sensores.
El clásico problema del broadcasting de consumo mÃnimo en redes ad hoc ha sido bien estudiado en la literatura. El problema considera un modelo de antena que permite transmitir a cualquier potencia elegida (hasta un máximo establecido por el dispositivo). Sin embargo, cuando se trabaja de forma especÃfica con redes de sensores, un vistazo al hardware actualmente disponible muestra que este modelo de antena no es demasiado realista. En este trabajo reformulamos el problema para el modelo de antena más habitual en redes de sensores. En este modelo, los niveles de potencia de transmisión se eligen de un conjunto finito de posibilidades. La siguiente contribución consiste en en la adaptación de un algoritmo de optimización por colonias de hormigas a la versión más realista del problema, también conocida como broadcasting de consumo mÃnimo con antenas realistas.
Los resultados obtenidos muestran que la ventaja de este método sobre heurÃsticas clásicas incluso crece cuando el número de posibles potencias de transmisión decrece. Además, se ha presentado una versión distribuida del algoritmo, que también se compara de forma bastante favorable contra las heurÃsticas centralizadas conocidas
ISBIS 2016: Meeting on Statistics in Business and Industry
This Book includes the abstracts of the talks presented at the 2016 International Symposium on Business and Industrial Statistics, held at Barcelona, June 8-10, 2016, hosted at the Universitat Politècnica de Catalunya - Barcelona TECH, by the Department of Statistics and Operations Research. The location of the meeting was at ETSEIB Building (Escola Tecnica Superior d'Enginyeria Industrial) at Avda Diagonal 647.
The meeting organizers celebrated the continued success of ISBIS and ENBIS society, and the meeting draw together the international community of statisticians, both academics and industry professionals, who share the goal of making statistics the foundation for decision making in business and related applications. The Scientific Program Committee was constituted by:
David Banks, Duke University
AmÃlcar Oliveira, DCeT - Universidade Aberta and CEAUL
Teresa A. Oliveira, DCeT - Universidade Aberta and CEAUL
Nalini Ravishankar, University of Connecticut
Xavier Tort Martorell, Universitat Politécnica de Catalunya, Barcelona TECH
Martina Vandebroek, KU Leuven
Vincenzo Esposito Vinzi, ESSEC Business Schoo
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
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