In this study, the effect of implementing Network Coding on the aggregated throughput in Wireless Mesh Networks, was examined. Wireless Mesh Networks (WMNs) are multiple hop wireless networks, where routing through any node is possible. The implication of this characteristic, is that messages flow across the points where it would have been terminated in conventional wireless networks. User nodes in conventional wireless networks only transmit and receive messages from an Access Point (AP), and discard any messages not intended for them. The result is an increase in the volume of network traffic through the links of WMNs. Additionally, the dense collection of multiple RF signals propagating through a shared wireless medium, contributes to the situation where the links become saturated at levels below their capacity. The need exists to examine methods that will improve the utilisation of the shared wireless medium in WMNs. Network Coding is a coding and decoding technique at the network level of the OSI stack, aimed to improve the boundaries of saturated links. The technique implies that the bandwidth is simultaneously shared amongst separate message flows, by combining these flows at common intermediate nodes. The number of transmissions needed to convey information through the network, is decreased by Network Coding. The result is in an improvement of the aggregated throughput. The research approach followed in this dissertation, includes the development of a model that investigates the aggregated throughput performance of WMNs. The scenario of the model, followed a typical example of indoors WMN implementations. Therefore, the physical environment representation of the network elements, included an indoors log–distance path loss channel model, to account for the different effects such as: power absorption through walls; and shadowing. Network functionality in the model was represented through a network flow programming problem. The problem was concerned with determining the optimal amount of flow represented through the links of the WMN, subject to constraints pertaining to the link capacities and mass balance at each node. The functional requirements of the model stated that multiple concurrent sessions were to be represented. This condition implied that the network flow problem had to be a multi–commodity network flow problem. Additionally, the model requirements stated that each session of flow should remain on a single path. This condition implied that the network flow problem had to be an integer programming problem. Therefore, the network flow programming problem of the model was considered mathematically equivalent to a multi–commodity integer programming problem. The complexity of multi–commodity integer programming problems is NP–hard. A heuristic solving method, Simulated Annealing, was implemented to solve the goal function represented by the network flow programming problem of the model. The findings from this research provide evidence that the implementation of Network Coding in WMNs, nearly doubles the level of the calculated aggregated throughput values. The magnitude of this throughput increase, can be further improved by additional manipulation of the network traffic dispersion. This is achieved by utilising link–state methods, rather than distance vector methods, to establish paths for the sessions of flow, present in the WMNs. / Thesis (M.Ing. (Computer and Electronical Engineering))--North-West University, Potchefstroom Campus, 2012.

Garg and Könemann developed a framework for computing multi-commodity maximum flow in a graph, later called a multiplicative weight update framework. Madry used this framework and exchanged Dijkstra’s algorithm to a dynamic graph algorithm for approximating the shortest paths through the graph. With this approachhe developed the fastest algorithm to date for calculating the multi-commodity maximum flow, with a running time of Õ(mnϵ2). This project have implemented the algorithm and compared it with a slightly modified version of the former fastest algorithm by Fleischer with a time complexity of Õ(m2ϵ2). The results show that Madry’s algorithms is slower than Fleischer’s algorithm in practice for graph with less than 100 million edges. This project also computed the space needed for the dynamic algorithms used in Madry’s algorithm and can show a resulting space complexity of O(n(n+m)log2n), compared to the space complexity of Fleischer’s algorithm of O(n). For a graph with 100 million edges, 50 million Gb of space is needed to use Madry’s algorithm, which is more than our test computers had. We can therefore conclude that Madry’s algorithm is not usable in real life today, both in terms of memory usage and time consumption. / Garg and Könemann utvecklade ett framework för att beräkna multi-commodity maximum flöde i en graf sedan kallat ett multiplicative weight update framework. Madry använde detta framework och bytte ut Dijkstra’s algoritm mot en dynamisk grafalgoritm för att kunna approximera kortaste vägen i grafen. Med detta angeppssätt utvecklade han den idag snabbaste algoritmen för beräkning av multicommodity maximum flöde med en tids komplexitet på Õ(mnϵ2). Det här projektet har implementerat hans algoritm och jämfört den med den tidigare snabbaste algoritmen skapad av Fleischer med en tidskomplexitet på Õ(m2ϵ2). Resultatet visar att Madrys algoritm är långsammare än Fleischers algoritm i praktiken för grafer med färre än 100 miljoner kanter. Detta projekt beräknade också minnesåtgången för de dynamiska algoritmerna i Madrys algorithm och kan visa en resulterade minneskomplexitet på O(n(n+m)log2n), jämfört med Fleischers algoritm på O(n). För en graf med 100 miljoner kanter så behövs 50 miljoner Gb av minne för att kunna använda Madrys algoritm, vilket var mer än våra testdatorer hade. Vi kan därför konstatera att Madrys algoritm inte är användbar i praktiken idag, både när det kommer till minnesanvändning och till tidsåtgång.

The purpose of this paper is to increase the routing efficiency of two previously separate commodity transports. By combining them in a common, multi-commodity network flow (MCNF). A Mixed Integer Linear Programming (MILP) model is used to minimize the mileage that is needed to fulfill demand in the different destinations of the transport network. Input needed for the model was mileage between destinations, which was obtained from open data. And the demand of respective commodity was received from documents and an estimation. To solve the stated problem approximations and simplifications was needed because it showed a NP-complete problem. The aim is to produce a result that shows a lower mileage than a reference measure from the present situation with separate transports. The result showed an optimized solution of 1939 km. Which was a difference of 1941 km from the reference measures, that summarized to 3880 km. Despite this the result from the model shows an effective optimization. Which makes the use of MILP for minimizing mileage inside a MCNF problem, a useful approach for solving the stated problem. / Syftet med arbetet var att effektivisera körsträckor för två tidigare separata transporter av olika produkter. Genom att kombinera dem till en gemensam transport i ett multi-commodity network flow (MCNF). Med en Mixed Integer Linear Programming (MILP) modell minimeras de körsträckor som krävs för att fylla efterfrågan i transportnätverkets adresser. In-data som krävdes för att en modell skulle kunna utföras var körsträckor mellan olika adresser, vilket hämtades från öppen data. Samt efterfrågan på produkter som erhölls från dokument och estimering.  Då problemet som skulle lösas visade på hög beräkningskomplexitet behövde ett antal approximationer och förenklingar verkställas. Målet var att visa på ett resultat där körsträckor hade förminskats relativt till ett referensmått från nuläget. Där resultatet visade på en optimerad lösning på 1939 km. Vilket var en differens på 1941 km från de referensmåttet som summerades till 3880 km. Modellens resultat visar trots det en effektiv optimering. Vilket gör att användningen av MILP för att minimera körsträckor inom MCNF problem, är ett effektivt tillvägagångssätt att lösa det motiverade problemet.