Approximating max-min linear programs with local algorithms

A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms to max-min LPs where the objective is to maximise $\min_k \sum_v c_{kv} x_v$ subject to $\sum_v a_{iv} x_v \le 1$ for each $i$ and $x_v \ge 0$ for each $v$. Here $c_{kv} \ge 0$, $a_{iv} \ge 0$, and the support sets $V_i = \{v : a_{iv} > 0 \}$, $V_k = \{v : c_{kv}>0 \}$, $I_v = \{i : a_{iv} > 0 \}$ and $K_v = \{k : c_{kv} > 0 \}$ have bounded size. In the distributed setting, each agent $v$ is responsible for choosing the value of $x_v$, and the communication network is a hypergraph $\mathcal{H}$ where the sets $V_k$ and $V_i$ constitute the hyperedges. We present inapproximability results for a wide range of structural assumptions; for example, even if $|V_i|$ and $|V_k|$ are bounded by some constants larger than 2, there is no local approximation scheme. To contrast the negative results, we present a local approximation algorithm which achieves good approximation ratios if we can bound the relative growth of the vertex neighbourhoods in $\mathcal{H}$.Comment: 16 pages, 2 figure

Fault-tolerant Coverage in Dense Wireless Sensor Networks

In this paper, we present methods to detect and recover from sensor failure in dense wireless sensor networks. In order to extend the lifetime of a sensor network while maintaining coverage, a minimal subset of the deployed sensors are kept active while the other sensors can enter a low power sleep state. Several distributed algorithms for coverage have been proposed in the literature. Faults are of particular concern in coverage algorithms since sensors go into a sleep state in order to conserve battery until woken up by active sensors. If these active sensors were to fail, this could lead to lapses in coverage that are unacceptable in critical applications. Also, most algorithms in the literature rely on an active sensor that is about to run out of battery waking up its neighbors to trigger a reshuffle in the network. However, this would not work in the case of unexpected failures since a sensor cannot predict the occurrence of such an event. We present detection and recovery from sensor failure in dense networks. Our algorithms exploit the density in the recovery scheme to improve coverage by 4-12% in the event of random failures. This fault tolerance comes at a small cost to the network lifetime with observed lifetime being reduced by 6-10% in our simulation studies

a Novel Energy Efficient, Distributed, Clustering based Network Coverage Method for Enormous WSN

Routing is one of the most important issues in wireless sensor networks. In order to transfer packets in the network effectively, a sound path between nodes should exist to reduce data transmission costs. A proper coverage algorithm is very critical to establish a suitable routing algorithm. Small set of nodes in a network is an important consideration for a coverage algorithm. This paper proposes a problem entitled 201C;inter and intra cluster dominating set based routing201D;. Clusters are made in large networks with numerous nodes to perform coverage in both inter and intra cluster levels. Cluster head as the manager of the cluster divides the cluster area into some cells and selects a node for each cell to work as the router of corresponding cell. Regardless to cluster head, the pivot nodes are also in charge of routing in the network. As the result of this algorithm, all the cluster heads and pivot nodes together make a group called dominating set which covers all over the entire region. This is designed to achieve full coverage and also its nodes establish routing backbone of the network. This is carried out in such a manner that every one of the network nodes has direct access to one of the selected pivots. The presented coverage algorithm is based on the platform of our last work in clustering (FEED). Using this technique reduces existing load of cluster head as well especially in huge networks and considerably decreases energy consumption of the regular nodes

Local approximability of max-min and min-max linear programs

In a max-min LP, the objective is to maximise ω subject to Ax ≤ 1, Cx ≥ ω1, and x ≥ 0. In a min-max LP, the objective is to minimise ρ subject to Ax ≤ ρ1, Cx ≥ 1, and x ≥ 0. The matrices A and C are nonnegative and sparse: each row ai of A has at most ΔI positive elements, and each row ck of C has at most ΔK positive elements. We study the approximability of max-min LPs and min-max LPs in a distributed setting; in particular, we focus on local algorithms (constant-time distributed algorithms). We show that for any ΔI ≥ 2, ΔK ≥ 2, and ε > 0 there exists a local algorithm that achieves the approximation ratio ΔI (1 − 1/ΔK) + ε. We also show that this result is the best possible: no local algorithm can achieve the approximation ratio ΔI (1 − 1/ΔK) for any ΔI ≥ 2 and ΔK ≥ 2.Peer reviewe

Pienen dominoivan joukon etsiminen tasoverkossa hajautetusti

Dominoiva joukko D on jonkin verkon solmujen osajoukko siten, että verkon jokainen solmu joko kuuluu D:hen tai on siihen kuuluvan solmun naapuri. Verkon pienimmän dominoivan joukon löytäminen verkossa on NP-kova ongelma. Mikäli algoritmi etsii pienintä joukkoa, jonka koko on x, mutta sen voidaan taata löytävän vain joukon, jonka koko on enintään ax jollakin vakiolla a, kutsutaan tulosjoukkoa oikean ratkaisun a-approksimaatioksi. Rajoitetussa verkossa voidaan löytää pienimmän dominoivan joukon approksimaatioita nopeasti. Hajautetussa laskennassa verkon solmut ovat rinnakkaisesti toimivia prosessoreita, jotka suorittavat kaikki samaa algoritmia. Vakioaikaisuudella tarkoitetaan hajautetun laskennan kontekstissa sitä, että prosessorit saavat vaihtaa naapuriprosessoriensa kanssa vain vakiomäärän viestejä. Algoritmi palauttaa valmistuttuaan jokaiselle solmulle tulosteen, esimerkiksi tiedon siitä, kuuluuko solmu dominoivaan joukkoon. Tässä tutkielmassa tarkastellaan pienimmän dominoivan joukon vakioaikaisia approksimaatioita tasoverkossa hajautetun laskennan näkökulmasta. Ensiksi tutkielmassa esitellään todistus, että ei ole olemassa hajautettua algoritmia, joka löytäisi (5 − epsilon)-approksimaation pienimmästä dominoivasta joukosta, kun epsilon > 0. Tämän jälkeen todistetaan, että myös tiukempi (7 − epsilon)-approksimaatioalaraja pätee. Lopuksi esitellään hajautettu algoritmi joka löytää ainakin 52-approksimaation pienimmästä dominoivasta joukosta tasoverkossa. Algoritmi käyttää uniikkeja tunnisteita eikä prosessorien välisten viestien kokoja ole rajoitettu. Algoritmin analyysissä yhdistetään Lenzenin et al. (2010) esittämä alkuperäinen analyysi ja Wawrzyniakin (2013) esittämä analyysin toisen osan parannus

Design and Implementation of a Communication Protocol to Improve Multimedia QoS and QoE in Wireless Ad Hoc Networks

[EN] This dissertation addresses the problem of multimedia delivery over multi-hop ad hoc wireless networks, and especially over wireless sensor networks. Due to their characteristics of low power consumption, low processing capacity and low memory capacity, they have major difficulties in achieving optimal quality levels demanded by end users in such communications. In the first part of this work, it has been carried out a study to determine the behavior of a variety of multimedia streams and how they are affected by the network conditions when they are transmitted over topologies formed by devices of different technologies in multi hop wireless ad hoc mode. To achieve this goal, we have performed experimental tests using a test bench, which combine the main codecs used in audio and video streaming over IP networks with different sound and video captures representing the characteristic patterns of multimedia services such as phone calls, video communications, IPTV and video on demand (VOD). With the information gathered in the laboratory, we have been able to establish the correlation between the induced changes in the physical and logical topology and the network parameters that measure the quality of service (QoS) of a multimedia transmission, such as latency, jitter or packet loss. At this stage of the investigation, a study was performed to determine the state of the art of the proposed protocols, algorithms, and practical implementations that have been explicitly developed to optimize the multimedia transmission over wireless ad hoc networks, especially in ad hoc networks using clusters of nodes distributed over a geographic area and wireless sensor networks. Next step of this research was the development of an algorithm focused on the logical organization of clusters formed by nodes capable of adapting to the circumstances of real-time traffic. The stated goal was to achieve the maximum utilization of the resources offered by the set of nodes that forms the network, allowing simultaneously sending reliably and efficiently all types of content through them, and mixing conventional IP data traffic with multimedia traffic with stringent QoS and QoE requirements. Using the information gathered in the previous phase, we have developed a network architecture that improves overall network performance and multimedia streaming. In parallel, it has been designed and programmed a communication protocol that allows implementing the proposal and testing its operation on real network infrastructures. In the last phase of this thesis we have focused our work on sending multimedia in wireless sensor networks (WSN). Based on the above results, we have adapted both the architecture and the communication protocol for this particular type of network, whose use has been growing hugely in recent years.[ES] Esta tesis doctoral aborda el problema de la distribución de contenidos multimedia a través de redes inalámbricas ad hoc multisalto, especialmente las redes inalámbricas de sensores que, debido a sus características de bajo consumo energético, baja capacidad de procesamiento y baja capacidad de memoria, plantean grandes dificultades para alcanzar los niveles de calidad óptimos que exigen los usuarios finales en dicho tipo de comunicaciones. En la primera parte de este trabajo se ha llevado a cabo un estudio para determinar el comportamiento de una gran variedad de flujos multimedia y como se ven afectados por las condiciones de la red cuando son transmitidos a través topologías formadas por dispositivos de diferentes tecnologías que se comunican en modo ad hoc multisalto inalámbrico. Para ello, se han realizado pruebas experimentales sobre una maqueta de laboratorio, combinando los principales códecs empleados en la transmisión de audio y video a través de redes IP con diversas capturas de sonido y video que representan patrones característicos de servicios multimedia tales como las llamadas telefónicas, videoconferencias, IPTV o video bajo demanda (VOD). Con la información reunida en el laboratorio se ha podido establecer la correlación entre los cambios inducidos en la topología física y lógica de la red con los parámetros que miden la calidad de servicio (QoS) de una transmisión multimedia, tales como la latencia el jitter o la pérdida de paquetes. En esta fase de la investigación se realiza un estudio para determinar el estado del arte de las propuestas de desarrollo e implementación de protocolos y algoritmos que se han generado de forma explícita para optimizar la transmisión de tráfico multimedia sobre redes ad hoc inalámbricas, especialmente en las redes inalámbricas de sensores y redes ad hoc utilizando clústeres de nodos distribuidos en un espacio geográfico. El siguiente paso en la investigación ha consistido en el desarrollo de un algoritmo propio para la organización lógica de clústeres formados por nodos capaces de adaptarse a las circunstancias del tráfico en tiempo real. El objetivo planteado es conseguir un aprovechamiento máximo de los recursos ofrecidos por el conjunto de nodos que forman la red, permitiendo de forma simultánea el envío de todo tipo de contenidos a través de ellos de forma confiable y eficiente, permitiendo la convivencia de tráfico de datos IP convencional con tráfico multimedia con requisitos exigentes de QoS y QoE. A partir de la información conseguida en la fase anterior, se ha desarrollado una arquitectura de red que mejora el rendimiento general de la red y el de las transmisiones multimedia de audio y video en particular. De forma paralela, se ha diseñado y programado un protocolo de comunicación que permite implementar el modelo y testear su funcionamiento sobre infraestructuras de red reales. En la última fase de esta tesis se ha dirigido la atención hacia la transmisión multimedia en las redes de sensores inalámbricos (WSN). Partiendo de los resultados anteriores, se ha adaptado tanto la arquitectura como el protocolo de comunicaciones para este tipo concreto de red, cuyo uso se ha extendido en los últimos años de forma considerable[CA] Esta tesi doctoral aborda el problema de la distribució de continguts multimèdia a través de xarxes sense fil ad hoc multi salt, especialment les xarxes sense fil de sensors que, a causa de les seues característiques de baix consum energètic, baixa capacitat de processament i baixa capacitat de memòria, plantegen grans dificultats per a aconseguir els nivells de qualitat òptims que exigixen els usuaris finals en eixos tipus de comunicacions. En la primera part d'este treball s'ha dut a terme un estudi per a determinar el comportament d'una gran varietat de fluxos multimèdia i com es veuen afectats per les condicions de la xarxa quan són transmesos a través topologies formades per dispositius de diferents tecnologies que es comuniquen en mode ad hoc multi salt sense fil. Per a això, s'han realitzat proves experimentals sobre una maqueta de laboratori, combinant els principals códecs empleats en la transmissió d'àudio i vídeo a través de xarxes IP amb diverses captures de so i vídeo que representen patrons característics de serveis multimèdia com son les cridades telefòniques, videoconferències, IPTV o vídeo baix demanda (VOD). Amb la informació reunida en el laboratori s'ha pogut establir la correlació entre els canvis induïts en la topologia física i lògica de la xarxa amb els paràmetres que mesuren la qualitat de servei (QoS) d'una transmissió multimèdia, com la latència el jitter o la pèrdua de paquets. En esta fase de la investigació es realitza un estudi per a determinar l'estat de l'art de les propostes de desenvolupament i implementació de protocols i algoritmes que s'han generat de forma explícita per a optimitzar la transmissió de tràfic multimèdia sobre xarxes ad hoc sense fil, especialment en les xarxes sense fil de sensors and xarxes ad hoc utilitzant clusters de nodes distribuïts en un espai geogràfic. El següent pas en la investigació ha consistit en el desenvolupament d'un algoritme propi per a l'organització lògica de clusters formats per nodes capaços d'adaptar-se a les circumstàncies del tràfic en temps real. L'objectiu plantejat és aconseguir un aprofitament màxim dels recursos oferits pel conjunt de nodes que formen la xarxa, permetent de forma simultània l'enviament de qualsevol tipus de continguts a través d'ells de forma confiable i eficient, permetent la convivència de tràfic de dades IP convencional amb tràfic multimèdia amb requisits exigents de QoS i QoE. A partir de la informació aconseguida en la fase anterior, s'ha desenvolupat una arquitectura de xarxa que millora el rendiment general de la xarxa i el de les transmissions multimèdia d'àudio i vídeo en particular. De forma paral¿lela, s'ha dissenyat i programat un protocol de comunicació que permet implementar el model i testejar el seu funcionament sobre infraestructures de xarxa reals. En l'última fase d'esta tesi s'ha dirigit l'atenció cap a la transmissió multimèdia en les xarxes de sensors sense fil (WSN). Partint dels resultats anteriors, s'ha adaptat tant l'arquitectura com el protocol de comunicacions per a aquest tipus concret de xarxa, l'ús del qual s'ha estés en els últims anys de forma considerable.Díaz Santos, JR. (2016). Design and Implementation of a Communication Protocol to Improve Multimedia QoS and QoE in Wireless Ad Hoc Networks [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/62162TESI

Mitigating hidden node problem in an IEEE 802.16 failure resilient multi-hop wireless backhaul

Backhaul networks are used to interconnect access points and further connect them to gateway nodes which are located in regional or metropolitan centres. Conventionally, these backhaul networks are established using metallic cables, optical fibres, microwave or satellite links. With the proliferation of wireless technologies, multi-hop wireless backhaul networks emerge as a potential cost effective and flexible solution to provide extended coverage to areas where the deployment of wired backhaul is difficult or cost-prohibitive, such as the difficult to access and sparsely populated remote areas, which have little or no existing wired infrastructure.Nevertheless, wireless backhaul networks are vulnerable to node or link failures. In order to ensure undisrupted traffic transmission even in the presence of failures, additional nodes and links are introduced to create alternative paths between each source and destination pair. Moreover, the deployment of such extra links and nodes requires careful planning to ensure that available network resources can be fully utilised, while still achieving the specified failure resilience with minimum infrastructure establishment cost.The majority of the current research efforts focus on improving the failure resilience of wired backhaul networks but little is carried out on the wireless counterparts. Most of the existing studies on improving the failure resilience of wireless backhaul networks concern energy-constrained networks such as the wireless sensor and ad hoc networks. Moreover, they tend to focus on maintaining the connectivity of the networks during failure, but neglecting the network performance. As such, it calls for a better approach to design a wireless backhaul network, which can meet the specified failure resilience requirement with minimum network cost, while achieving the specified quality of service (QoS).In this study, a failure resilient wireless backhaul topology, taking the form of a ladder network, is proposed to connect a remote community to a gateway node located in a regional or metropolitan centre. This topology is designed with the use of a minimum number of nodes. Also, it provides at least one backup path between each node pair. With the exception of a few failure scenarios, the proposed ladder network can sustain multiple simultaneous link or node failures. Furthermore, it allows traffic to traverse a minimum number of additional hops to arrive at the destination during failure conditions.WiMax wireless technology, based on the IEEE 802.16 standard, is applied to the proposed ladder network of different hop counts. This wireless technology can operate in either point-to-multipoint single-hop mode or multi-hop mesh mode. For the latter, coordinated distributed scheduling involving a three-way handshake procedure is used for resource allocation. Computer simulations are used to extensively evaluate the performance of the ladder network. It is shown that the three-way handshake suffers from severe hidden node problem, which restrains nodes from data transmission for long period of time. As a result, data packets accumulate in the buffer queue of the affected nodes and these packets will be dropped when the buffer overflows. This in turn results in the degradation of the network throughput and increase of average transmission delay.A new scheme called reverse notification (RN) is proposed to overcome the hidden node problem. With this new scheme, all the nodes will be informed of the minislots requested by their neighbours. This will prevent the nodes from making the same request and increase the chance for the nodes to obtain all their requested resources, and start transmitting data as soon as the handshake is completed. Computer simulations have verified that the use of this RN can significantly reduce the hidden terminal problem and thus increase network throughput, as well as reduce transmission delay.In addition, two new schemes, namely request-resend and dynamic minislot allocation, are proposed to further mitigate the hidden node problem as it deteriorates during failure. The request-resend scheme is proposed to solve the hidden node problem when the RN message failed to arrive in time at the destined node to prevent it from sending a conflicting request. On the other hand, the dynamic minislot allocation scheme is proposed to allocate minislots to a given node according to the amount of traffic that it is currently servicing. It is shown that these two schemes can greatly enhance the network performance under both normal and failure conditions.The performance of the ladder network can be further improved by equipping each node with two transceivers to allow them to transmit concurrently on two different frequency channels. Moreover, a two-channel two-transceiver channel assignment (TTDCA) algorithm is proposed to allocate minislots to the nodes. When operating with this algorithm, a node uses only one of its two transceivers to transmit control messages during control subframe and both transceivers to transmit data packets during data subframe. Also, the frequency channels of the nodes are pre-assigned to more effectively overcome the hidden node problem. It is shown that the use of the TTDCA algorithm, in conjunction with the request-resend and RN schemes, is able to double the maximum achievable throughput of the ladder network, when compared to the single channel case. Also, the throughput remains constant regardless of the hop counts.The TTDCA algorithm is further modified to make use of the second transceiver at each node to transmit control messages during control subframe. Such an approach is referred to as enhanced TTDCA (ETTDCA) algorithm. This algorithm is effective in reducing the duration needed to complete the three-way handshake without sacrificing network throughput. It is shown that the application of the ETTDCA algorithm in ladder networks of different hop counts has greatly reduced the transmission delay to a value which allows the proposed network to not only relay a large amount of data traffic but also delay-sensitive traffics. This suggests that the proposed ladder network is a cost effective solution, which can provide the necessary failure resilience and specified QoS, for delivering broadband multimedia services to the remote rural communities