Hulkade ühendamine
Date
2014
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Abstract
Olgu erinevad seadmed, mis omavad failide hulga erinevaid alamhulki. Talletades neid hulki pilves, kaasneb sellega failide sünkroniseerimise probleem. Eesmärgiks on igas seadmes leida nende hulkade ühend.
Naiivne lahendus sellele probleemile on kõikide hulkade edastamine kõikide osapoolte poolt. Selline lähenemine toob kaasa suure andmeedastuskeerukuse. Soovitav oleks leida algoritm, mille andmeedastuskeerukus oleks proportsionaalne hulkade sümmeetrilise vahe suurusega, mis on tüüpiliselt väike võrreldes kõikide failide arvuga.
Me defineerime mitmeid erinevaid andmete edastamise võrkude mudeleid. Efektiivsed algoritmid hulkade ühendamiseks on teada kahe osapoolega võrkude jaoks, kuid sarnased algoritmid üldiste võrkude jaoks on veel teadmata.
Me uurime võrgu topoloogiate ja hulkade ühendamise algoritmide vahelist seost. Me paneme tähele, et andmeedastuskeerukust on võimalik vähendada spetsiifilise topoloogiaga võrkudes.
Me samuti uurime juhtmega võrkudes iteratsioonide minimiseerimise ülesannet. Me defineerime ühenduste kaaludena ühenduste otspunktideks olevates seadmetes asuvate erinevate failide arvu. Me uurime katseliselt maksimaalsete kaalude valikumeetodi efektiivsust suhtlevate seadmepaaride valikuks. Tulemused viitavad, et see algoritm annab paremaid tulemusi võrreldes suhtlevate seadmepaaride juhusliku valikuga.
Selle magistritöö põhitulemuseks on algebraline analüütiline raamistik hulkade ühendamise algoritmide uurimiseks juhtmeta võrkudes. Raamistiku abil on võimalik optimeerida hulkade ühendamise algoritme, mis kasutavad lineaarselt kodeeritud teateid. See lähenemine üritab minimiseerida iteratsioonide ja edastavate teadete arvu.
Assume that we have several devices with different subsets of a set of files. The problem of file synchronization arises in cloud storage. The goal is to find a union of the sets at each of these devices. The naive solution to the problem is to transmit the whole sets by all parties in the network. This, however, results in high communicational complexity. It would be desirable to find an algorithm with communicational complexity that is proportional to the size of the symmetric difference of the sets, which is typically small when compared to the total number of files. We define a number of communication network models. Several efficient algorithms for set reconciliation over a network with two devices have been described in the literature, but similar algorithms for general networks are still unknown. We study the connection between the network topologies and the communicational cost in the set reconciliation algorithms. We observe that it is possible to reduce the communicational cost in networks of specific topology. We also study a problem of minimization of a number of communication rounds in a wired network. We define weights on the edges of the graph according to the number of different files in the communicating devices. Then, we experimentally test the efficiency of choosing the communicating pairs using maximum weight matching. The results imply that this algorithm provides better results than its counterpart which chooses the communicating pairs randomly. The main result of this Thesis is an algebraic analytical framework for studying the set reconciliation algorithms in wireless networks. This frameworks allows for optimizing set reconciliation protocols which use linearly coded messages. This approach aims at minimizing the number of iterations and the number of transmissions during each iteration.
Assume that we have several devices with different subsets of a set of files. The problem of file synchronization arises in cloud storage. The goal is to find a union of the sets at each of these devices. The naive solution to the problem is to transmit the whole sets by all parties in the network. This, however, results in high communicational complexity. It would be desirable to find an algorithm with communicational complexity that is proportional to the size of the symmetric difference of the sets, which is typically small when compared to the total number of files. We define a number of communication network models. Several efficient algorithms for set reconciliation over a network with two devices have been described in the literature, but similar algorithms for general networks are still unknown. We study the connection between the network topologies and the communicational cost in the set reconciliation algorithms. We observe that it is possible to reduce the communicational cost in networks of specific topology. We also study a problem of minimization of a number of communication rounds in a wired network. We define weights on the edges of the graph according to the number of different files in the communicating devices. Then, we experimentally test the efficiency of choosing the communicating pairs using maximum weight matching. The results imply that this algorithm provides better results than its counterpart which chooses the communicating pairs randomly. The main result of this Thesis is an algebraic analytical framework for studying the set reconciliation algorithms in wireless networks. This frameworks allows for optimizing set reconciliation protocols which use linearly coded messages. This approach aims at minimizing the number of iterations and the number of transmissions during each iteration.