16,005 research outputs found
Exact two-terminal reliability of some directed networks
The calculation of network reliability in a probabilistic context has long
been an issue of practical and academic importance. Conventional approaches
(determination of bounds, sums of disjoint products algorithms, Monte Carlo
evaluations, studies of the reliability polynomials, etc.) only provide
approximations when the network's size increases, even when nodes do not fail
and all edges have the same reliability p. We consider here a directed, generic
graph of arbitrary size mimicking real-life long-haul communication networks,
and give the exact, analytical solution for the two-terminal reliability. This
solution involves a product of transfer matrices, in which individual
reliabilities of edges and nodes are taken into account. The special case of
identical edge and node reliabilities (p and rho, respectively) is addressed.
We consider a case study based on a commonly-used configuration, and assess the
influence of the edges being directed (or not) on various measures of network
performance. While the two-terminal reliability, the failure frequency and the
failure rate of the connection are quite similar, the locations of complex
zeros of the two-terminal reliability polynomials exhibit strong differences,
and various structure transitions at specific values of rho. The present work
could be extended to provide a catalog of exactly solvable networks in terms of
reliability, which could be useful as building blocks for new and improved
bounds, as well as benchmarks, in the general case
Solving Parity Games in Scala
Parity games are two-player games, played on directed graphs, whose nodes are labeled with priorities. Along a play, the maximal priority occurring infinitely often determines the winner. In the last two decades, a variety of algorithms and successive optimizations have been proposed. The majority of them have been implemented in PGSolver, written in OCaml, which has been elected by the community as the de facto platform to solve efficiently parity games as well as evaluate their performance in several specific cases.
PGSolver includes the Zielonka Recursive Algorithm that has been shown to perform better than the others in randomly generated games. However, even for arenas with a few thousand of nodes (especially over dense graphs), it requires minutes to solve the corresponding game.
In this paper, we deeply revisit the implementation of the recursive algorithm introducing several improvements and making use of Scala Programming Language. These choices have been proved to be very successful, gaining up to two orders of magnitude in running time
Algorithms for Replica Placement in High-Availability Storage
A new model of causal failure is presented and used to solve a novel replica
placement problem in data centers. The model describes dependencies among
system components as a directed graph. A replica placement is defined as a
subset of vertices in such a graph. A criterion for optimizing replica
placements is formalized and explained. In this work, the optimization goal is
to avoid choosing placements in which a single failure event is likely to wipe
out multiple replicas. Using this criterion, a fast algorithm is given for the
scenario in which the dependency model is a tree. The main contribution of the
paper is an dynamic programming algorithm for placing
replicas on a tree with vertices. This algorithm exhibits the
interesting property that only two subproblems need to be recursively
considered at each stage. An greedy algorithm is also briefly
reported.Comment: 22 pages, 7 figures, 4 algorithm listing
A Bootstrap Method for Identifying and Evaluating a Structural Vector Autoregression
Graph-theoretic methods of causal search based in the ideas of Pearl (2000), Spirtes,
Glymour, and Scheines (2000), and others have been applied by a number of researchers
to economic data, particularly by Swanson and Granger (1997) to the problem of finding
a data-based contemporaneous causal order for the structural autoregression (SVAR),
rather than, as is typically done, assuming a weakly justified Choleski order. Demiralp
and Hoover (2003) provided Monte Carlo evidence that such methods were effective,
provided that signal strengths were sufficiently high. Unfortunately, in applications to
actual data, such Monte Carlo simulations are of limited value, since the causal structure
of the true data-generating process is necessarily unknown. In this paper, we present a
bootstrap procedure that can be applied to actual data (i.e., without knowledge of the true
causal structure). We show with an applied example and a simulation study that the
procedure is an effective tool for assessing our confidence in causal orders identified by
graph-theoretic search procedures.vector autoregression (VAR), structural vector autoregression (SVAR),causality, causal order, Choleski order, causal search algorithms, graph-theoretic methods
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