8,681 research outputs found
On dynamic breadth-first search in external-memory
We provide the first non-trivial result on dynamic breadth-first search (BFS) in external-memory: For general sparse undirected graphs of initially nodes and O(n) edges and monotone update sequences of either edge insertions or edge deletions, we prove an amortized high-probability bound of O(n/B^{2/3}+\sort(n)\cdot \log B) I/Os per update. In contrast, the currently best approach for static BFS on sparse undirected graphs requires \Omega(n/B^{1/2}+\sort(n)) I/Os. 1998 ACM Subject Classification: F.2.2. Key words and phrases: External Memory, Dynamic Graph Algorithms, BFS, Randomization
Fatalism as a Metaphysical Thesis
Even though fatalism has been an intermittent topic of philosophy since Greek antiquity, this paper argues that fate ought to be of little concern to metaphysicians. Fatalism is neither an interesting metaphysical thesis in its own right, nor can it be identified with theses that are, such as realism about the future or determinism
Crossed module actions on continuous trace -algebras
We lift an action of a torus on the spectrum of a continuous
trace algebra to an action of a certain crossed module of Lie groups that is an
extension of . We compute equivariant Brauer and Picard groups
for this crossed module and describe the obstruction to the existence of an
action of in our framework.Comment: 27 pages, added background material about T-Duality, added
references, extended section about non-associative C*-algebra
An O(n^{2.75}) algorithm for online topological ordering
We present a simple algorithm which maintains the topological order of a
directed acyclic graph with n nodes under an online edge insertion sequence in
O(n^{2.75}) time, independent of the number of edges m inserted. For dense
DAGs, this is an improvement over the previous best result of O(min(m^{3/2}
log(n), m^{3/2} + n^2 log(n)) by Katriel and Bodlaender. We also provide an
empirical comparison of our algorithm with other algorithms for online
topological sorting. Our implementation outperforms them on certain hard
instances while it is still competitive on random edge insertion sequences
leading to complete DAGs.Comment: 20 pages, long version of SWAT'06 pape
On Dynamic Breadth-First Search in External-Memory
We provide the first non-trivial result on dynamic breadth-first
search (BFS) in external-memory: For general sparse undirected
graphs of initially nodes and edges and monotone update
sequences of either edge insertions or edge
deletions, we prove an amortized high-probability bound of
I/Os per update. In contrast,
the currently best approach for static BFS on sparse undirected
graphs requires I/Os
Design and analysis of sequential and parallel single-source shortest-paths algorithms
We study the performance of algorithms for the Single-Source Shortest-Paths (SSSP) problem on graphs with n nodes and m edges with nonnegative random weights. All previously known SSSP algorithms for directed graphs required superlinear time. Wie give the first SSSP algorithms that provably achieve linear O(n-m)average-case execution time on arbitrary directed graphs with random edge weights. For independent edge weights, the linear-time bound holds with high probability, too. Additionally, our result implies improved average-case bounds for the All-Pairs Shortest-Paths (APSP) problem on sparse graphs, and it yields the first theoretical average-case analysis for the "Approximate Bucket Implementation" of Dijkstra\u27s SSSP algorithm (ABI-Dijkstra). Futhermore, we give constructive proofs for the existence of graph classes with random edge weights on which ABI-Dijkstra and several other well-known SSSP algorithms require superlinear average-case time. Besides the classical sequential (single processor) model of computation we also consider parallel computing: we give the currently fastest average-case linear-work parallel SSSP algorithms for large graph classes with random edge weights, e.g., sparse rondom graphs and graphs modeling the WWW, telephone calls or social networks.In dieser Arbeit untersuchen wir die Laufzeiten von Algorithmen fĂŒr das KĂŒrzeste-Wege Problem (Single-Source Shortest-Paths, SSSP) auf Graphen mit n Knoten, M Kanten und nichtnegativen zufĂ€lligen Kantengewichten. Alle bisherigen SSSP Algorithmen benötigen auf gerichteten Graphen superlineare Zeit. Wir stellen den ersten SSSP Algorithmus vor, der auf beliebigen gerichteten Graphen mit zufĂ€lligen Kantengewichten eine beweisbar lineare average-case-KomplexitĂ€t
O(n+m)aufweist. Sind die Kantengewichte unabhĂ€ngig, so wird die lineare Zeitschranke auch mit hoher Wahrscheinlichkeit eingehalten. AuĂerdem impliziert unser Ergebnis verbesserte average-case-Schranken fĂŒr das All-Pairs Shortest-Paths (APSP) Problem auf dĂŒnnen Graphen und liefert die erste theoretische average-case-Analyse fĂŒr die "Approximate Bucket Implementierung" von Dijkstras SSSP Algorithmus (ABI-Dijkstra). Weiterhin fĂŒhren wir konstruktive Existenzbeweise fĂŒr Graphklassen mit zufĂ€lligen Kantengewichten, auf denen ABI-Dijkstra und mehrere andere bekannte SSSP Algorithmen durchschnittlich superlineare Zeit benötigen. Neben dem klassischen seriellen (Ein-Prozessor) Berechnungsmodell betrachten wir auch Parallelverarbeitung; fĂŒr umfangreiche Graphklassen mit zufĂ€lligen Kantengewichten wie z.B. dĂŒnne Zufallsgraphen oder Modelle fĂŒr das WWW, Telefonanrufe oder soziale Netzwerke stellen wir die derzeit schnellsten parallelen SSSP Algorithmen mit durchschnittlich linearer Arbeit vor
Time as a logical space (Proceedings of the CAPE International Workshops, 2013. Part II: The CAPEăInternational Conference âA Frontier of Philosophy of Timeâ)
30th Nov. and 1st Dec. 2013 at Kyoto University. Organizer: Takeshi Sako
A structural analysis of the A5/1 state transition graph
We describe efficient algorithms to analyze the cycle structure of the graph
induced by the state transition function of the A5/1 stream cipher used in GSM
mobile phones and report on the results of the implementation. The analysis is
performed in five steps utilizing HPC clusters, GPGPU and external memory
computation. A great reduction of this huge state transition graph of 2^64
nodes is achieved by focusing on special nodes in the first step and removing
leaf nodes that can be detected with limited effort in the second step. This
step does not break the overall structure of the graph and keeps at least one
node on every cycle. In the third step the nodes of the reduced graph are
connected by weighted edges. Since the number of nodes is still huge an
efficient bitslice approach is presented that is implemented with NVIDIA's CUDA
framework and executed on several GPUs concurrently. An external memory
algorithm based on the STXXL library and its parallel pipelining feature
further reduces the graph in the fourth step. The result is a graph containing
only cycles that can be further analyzed in internal memory to count the number
and size of the cycles. This full analysis which previously would take months
can now be completed within a few days and allows to present structural results
for the full graph for the first time. The structure of the A5/1 graph deviates
notably from the theoretical results for random mappings.Comment: In Proceedings GRAPHITE 2012, arXiv:1210.611
INTEGRATING SUSTAINABILITY IN AGRICULTURE - TRADE-OFFS AND ECONOMIC CONSEQUENCES DEMONSTRATED WITH A FARM MODEL IN BAVARIA
Within the German "Research Alliance on Agroecosystems Munich" (Forschungsverbund Agrarökosysteme MĂŒnchen, FAM) optimal land use strategies are investigated since 1990 in terms of minimization of environmental impacts and maximization of profit from agricultural lands (Auerswald et al. 2000). For this purpose a conventional agricultural land use system was converted into two more sustainable forms of land use. One part of the farm was converted into an integrated land use system with reduced tillage, direct seeding methods and catch crops to minimize nutrient losses and to prevent soil erosion hazards. The other part of the farm was converted into a biological land use system with the omission of mineral fertilizers and pesticides and the enrichment of crop rotation. In order to evaluate changes in the state of the agroecosystem a goal and indicator system was elaborated which was aimed to represent important issues of sustainable agriculture. With the help of the goal and indicator system the impact of land use on issues of sustainability can be assessed. The indicators are furthermore integrated into a farm model to assess the implications of the realization of environmental issues in agriculture. For this purpose the model system MODAM (Zander & KĂ€chele 1999) was used to compare different land use options at the farm level. The model system simulates agricultural land use, calculates the economic returns and runs farm optimizations with a linear programming tool. The integration of agro-environmental indicators in the model framework enables a multiple goal optimization and the calculation of trade-offs. For this study soil erosion was assessed with the algorithms of a site-specifically adapted version of the USLE (ABAG, Schwertmann et al. 1987). Optimization runs show, that e.g. soil conservation measures may not only improve soil conservation, but also the economic situation. A slight improvement of soil conservation results in marginal opportunity costs for the farm. With the realization of a higher level of soil protection opportunity costs rise exponentially. The calculated opportunity costs can give valuable hints on bottlenecks of the realization of sustainable agriculture and help to identify reasonable incentives for a better agriculture. Furthermore conflicts between divagating goals can be identified to find optimal pathways of a sustainable development of agriculture.Environmental Economics and Policy, Farm Management,
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