Online Algorithms for Multi-Level Aggregation

In the Multi-Level Aggregation Problem (MLAP), requests arrive at the nodes of an edge-weighted tree T, and have to be served eventually. A service is defined as a subtree X of T that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the TCP Acknowledgment Problem, while for trees of depth 2, it is equivalent to the Joint Replenishment Problem. Aggregation problem for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and in supply-chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant competitive online algorithm for networks of arbitrary (fixed) number of levels. The competitive ratio is O(D^4 2^D), where D is the depth of T. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines. We also show several additional lower and upper bound results for some special cases of MLAP, including the Single-Phase variant and the case when the tree is a path

New results on multi-level aggregation

International audienceIn the Multi-Level Aggregation Problem (MLAP ), requests for service arrive at the nodes of an edge-weighted rooted tree . Each service is represented by a subtree X of that contains its root. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs a waiting cost between its arrival and service time. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. The currently best online algorithms for the MLAP achieve competitive ratios polynomial in the tree depth, while the best lower bound is only 3.618. In this paper, we report some progress towards closing this gap, by improving this lower bound and providing several tight bounds for restricted variants of MLAP: (1) We first study a Single-Phase variant of MLAP where all requests are released at the beginning and expire at some unknown time θ, for which we provide an online algorithm with optimal competitive ratio of 4. (2) We prove a lower bound of 4 on the competitive ratio for MLAP, even when the tree is a path. We complement this with a matching upper bound for the deadline variant of MLAP on paths. Additionally, we provide two results for the offline case: (3) We prove that the Single-Phase variant can be solved optimally in polynomial time, and (4) we give a simple 2-approximation algorithm for offline MLAP with deadlines

Online algorithms for multi-level aggregation

In the multilevel aggregation problem (MLAP), requests arrive at the nodes of an edge-weighted tree T and have to be served eventually. A service is defined as a subtree X of T that contains the root of T. This subtree X serves all requests that are pending in the nodes of X, and the cost of this service is equal to the total weight of X. Each request also incurs waiting cost between its arrival and service times. The objective is to minimize the total waiting cost of all requests plus the total cost of all service subtrees. MLAP is a generalization of some well-studied optimization problems; for example, for trees of depth 1, MLAP is equivalent to the Transmission Control Protocol acknowledgment problem, whereas for trees of depth 2, it is equivalent to the joint replenishment problem. Aggregation problems for trees of arbitrary depth arise in multicasting, sensor networks, communication in organization hierarchies, and supply chain management. The instances of MLAP associated with these applications are naturally online, in the sense that aggregation decisions need to be made without information about future requests. Constant-competitive online algorithms are known for MLAP with one or two levels. However, it has been open whether there exist constant-competitive online algorithms for trees of depth more than 2. Addressing this open problem, we give the first constant-competitive online algorithm for trees of arbitrary (fixed) depth. The competitive ratio is O(D42D), where D is the depth of T. The algorithm works for arbitrary waiting cost functions, including the variant with deadlines

Abordagens autonômicas para qualidade de serviço da comunicação em redes de sensores sem fio densas com requisitos temporais

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2010Em Redes de Sensores Sem Fio (RSSF), a fusão de dados com restrições temporais pode ser utilizada para gerar visões globais da rede e ainda compensar a baixa confiabilidade individual dos nodos. Entretanto, os nodos de uma rede com grande quantidade de nodos devem ser capazes de se auto-otimizar e auto-organizar sem a interferência de operadores humanos. Nesta tese, apresentamos diversas abordagens autonômicas para garantia de QoS em RSSF com aplicações de fusão de dados com restrições temporais. As abordagens foram validadas através de simulações utilizando TrueTime e testes em protótipos de RSSF. Uma das abordagens autonômicas utiliza algoritmo de aprendizado de máquina baseado em algoritmos genéticos. Esses algoritmos são inspirados na teoria da seleção natural e conseguem otimizar parâmetros como a eficiência da comunicação mesmo em problemas de otimização multi-objetivo. Abordagens autonômicas cientes de energia, assim como abordagens autonômicas mais simples, são também apresentadas. Uma vez que nossas abordagens foram modeladas para atuar na camada de aplicação de dispositivos compatíveis com o padrão IEEE 802.15.4, tornam-se de fácil implementação em dispositivos disponíveis comercialmente. As abordagens apresentadas mostraram um desempenho bem superior ao desempenho do protocolo IEEE 802.15.4

Diseño, Especificación, Validación y Aplicación de una Arquitectura modular de gestión de Redes Inalámbricas de Sensores

Durante los últimos años las redes de sensores inalámbricas han sido objeto, como consecuencia de un creciente interés comercial, de una intensa actividad de investigación que ha determinado relevantes avances tanto en la tecnología base como en los aspectos de ingeniería a todos los niveles. Las redes de sensores inalámbricas se basan en el concepto de nodo sensor autónomo de bajo coste que proporciona recursos limitados en términos de cálculo y capacidad de almacenamiento de información, baja potencia de transmisión y sensorica avanzada. Se caracterizan por el tamaño extremadamente reducido y una ingeniería orientada a la eficiencia energética. A pesar de la disponibilidad de soluciones altamente avanzadas, caracterizadas por la eficiencia y la flexibilidad, la difusión comercial masiva se ha planteado más veces como hipótesis plausible y además parece tardar en concretarse de forma definitiva. Las principales causas están relacionadas, directamente o indirectamente, con dos factores: coste elevado y falta de suficiente fiabilidad/robustez. Una de las consecuencias del desarrollo de arquitecturas "ad-hoc" que caracteriza actualmente las redes de sensores inalámbricas es la de garantizar una gran cantidad de óptimos locales siendo la causa principal de una preocupante ausencia de estándares tanto en términos de protocolos de comunicación como en términos de organización y representación de información. También nuevos modelos de negocio y de explotación dentro de las organizaciones virtuales de última generación son actualmente temas de atención en el seno de la comunidad científica internacional. Este trabajo se sitúa en el marco de las últimas líneas de investigación orientadas a conciliar soluciones avanzadas, caracterizadas por una ingeniería innovadora, con su aplicación efectiva en el mundo realPileggi ., SF. (2011). Diseño, Especificación, Validación y Aplicación de una Arquitectura modular de gestión de Redes Inalámbricas de Sensores [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10740Palanci