921 research outputs found
Parallel Transitive Closure and Point Location in Planar Structures
AMS(MOS) subject classifications. 68E05, 68C05, 68C25Parallel algorithms for several graph and geometric problems are presented, including transitive closure and topological sorting in planar st-graphs, preprocessing planar subdivisions for point location queries, and construction of visibility representations and drawings of planar graphs.
Most of these algorithms achieve optimal O(logn) running time using n/logn processors in the EREW PRAM model, n being the number of vertices
Join-Reachability Problems in Directed Graphs
For a given collection G of directed graphs we define the join-reachability
graph of G, denoted by J(G), as the directed graph that, for any pair of
vertices a and b, contains a path from a to b if and only if such a path exists
in all graphs of G. Our goal is to compute an efficient representation of J(G).
In particular, we consider two versions of this problem. In the explicit
version we wish to construct the smallest join-reachability graph for G. In the
implicit version we wish to build an efficient data structure (in terms of
space and query time) such that we can report fast the set of vertices that
reach a query vertex in all graphs of G. This problem is related to the
well-studied reachability problem and is motivated by emerging applications of
graph-structured databases and graph algorithms. We consider the construction
of join-reachability structures for two graphs and develop techniques that can
be applied to both the explicit and the implicit problem. First we present
optimal and near-optimal structures for paths and trees. Then, based on these
results, we provide efficient structures for planar graphs and general directed
graphs
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Dynamic Data Structures for Series Parallel Digraphs
We consider the problem of dynamically maintaining general series parallel directed acyclic graphs (GSP dags), two-terminal series parallel directed acyclic graphs (TTSP dags) and looped series parallel directed graphs (looped SP digraphs). We present data structures for updating (by both inserting and deleting either a group of edges or vertices) GSP dags, TTSP clags and looped SP digraphs of m edges and n vertices in O( log n) worst-case time. The time required to check whether there is a path between two given vertices is O(log n), while a path of length k can be traced out in O(k + log n) time. For GSP and TTSP dags, our data structures are able to report a regular expression describing all the paths between two vertices x and y in O(h + log n), where h ≤ n is the total number of vertices which are contained in paths from x to y. Although GSP dags can have as many as O(n2) edges, we use an implicit representation which requires only O(n) space. Motivations for studying dynamic graphs arise in several areas, such as communication networks, Incremental compilation environments and the design of very high level languages, while the dynamic maintenance of series parallel graphs is also relevant in reducible flow diagrams
Privaatsust säilitavad paralleelarvutused graafiülesannete jaoks
Turvalisel mitmeosalisel arvutusel põhinevate reaalsete privaatsusrakenduste loomine on SMC-protokolli arvutusosaliste ümmarguse keerukuse tõttu keeruline. Privaatsust säilitavate tehnoloogiate uudsuse ja nende probleemidega kaasnevate suurte arvutuskulude tõttu ei ole paralleelseid privaatsust säilitavaid graafikualgoritme veel uuritud. Graafikalgoritmid on paljude arvutiteaduse rakenduste selgroog, nagu navigatsioonisüsteemid, kogukonna tuvastamine, tarneahela võrk, hüperspektraalne kujutis ja hõredad lineaarsed lahendajad. Graafikalgoritmide suurte privaatsete andmekogumite töötlemise kiirendamiseks ja kõrgetasemeliste arvutusnõuete täitmiseks on vaja privaatsust säilitavaid paralleelseid algoritme. Seetõttu esitleb käesolev lõputöö tipptasemel protokolle privaatsuse säilitamise paralleelarvutustes erinevate graafikuprobleemide jaoks, ühe allika lühima tee, kõigi paaride lühima tee, minimaalse ulatuva puu ja metsa ning algebralise tee arvutamise. Need uued protokollid on üles ehitatud kombinatoorsete ja algebraliste graafikualgoritmide põhjal lisaks SMC protokollidele. Nende protokollide koostamiseks kasutatakse ka ühe käsuga mitut andmeoperatsiooni, et vooru keerukust tõhusalt vähendada. Oleme väljapakutud protokollid juurutanud Sharemind SMC platvormil, kasutades erinevaid graafikuid ja võrgukeskkondi. Selles lõputöös kirjeldatakse uudseid paralleelprotokolle koos nendega seotud algoritmide, tulemuste, kiirendamise, hindamiste ja ulatusliku võrdlusuuringuga. Privaatsust säilitavate ühe allika lühimate teede ja minimaalse ulatusega puuprotokollide tegelike juurutuste tulemused näitavad tõhusat meetodit, mis vähendas tööaega võrreldes varasemate töödega sadu kordi. Lisaks ei ole privaatsust säilitavate kõigi paaride lühima tee protokollide hindamine ja ulatuslik võrdlusuuringud sarnased ühegi varasema tööga. Lisaks pole kunagi varem käsitletud privaatsust säilitavaid metsa ja algebralise tee arvutamise protokolle.Constructing real-world privacy applications based on secure multiparty computation is challenging due to the round complexity of the computation parties of SMC protocol. Due to the novelty of privacy-preserving technologies and the high computational costs associated with these problems, parallel privacy-preserving graph algorithms have not yet been studied. Graph algorithms are the backbone of many applications in computer science, such as navigation systems, community detection, supply chain network, hyperspectral image, and sparse linear solvers. In order to expedite the processing of large private data sets for graphs algorithms and meet high-end computational demands, privacy-preserving parallel algorithms are needed. Therefore, this Thesis presents the state-of-the-art protocols in privacy-preserving parallel computations for different graphs problems, single-source shortest path (SSSP), All-pairs shortest path (APSP), minimum spanning tree (MST) and forest (MSF), and algebraic path computation. These new protocols have been constructed based on combinatorial and algebraic graph algorithms on top of the SMC protocols. Single-instruction-multiple-data (SIMD) operations are also used to build those protocols to reduce the round complexities efficiently. We have implemented the proposed protocols on the Sharemind SMC platform using various graphs and network environments. This Thesis outlines novel parallel protocols with their related algorithms, the results, speed-up, evaluations, and extensive benchmarking. The results of the real implementations of the privacy-preserving single-source shortest paths and minimum spanning tree protocols show an efficient method that reduced the running time hundreds of times compared with previous works. Furthermore, the evaluation and extensive benchmarking of privacy-preserving All-pairs shortest path protocols are not similar to any previous work. Moreover, the privacy-preserving minimum spanning forest and algebraic path computation protocols have never been addressed before.https://www.ester.ee/record=b555865
Dynamic Maintenance of Planar Digraphs, with Applications
Coordinated Science Laboratory was formerly known as Control Systems LaboratoryNational Science Foundation / ECS-84-10902Joint Services Electronics Program / N00014-84-C-014
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