35,022 research outputs found
Transient Reward Approximation for Continuous-Time Markov Chains
We are interested in the analysis of very large continuous-time Markov chains
(CTMCs) with many distinct rates. Such models arise naturally in the context of
reliability analysis, e.g., of computer network performability analysis, of
power grids, of computer virus vulnerability, and in the study of crowd
dynamics. We use abstraction techniques together with novel algorithms for the
computation of bounds on the expected final and accumulated rewards in
continuous-time Markov decision processes (CTMDPs). These ingredients are
combined in a partly symbolic and partly explicit (symblicit) analysis
approach. In particular, we circumvent the use of multi-terminal decision
diagrams, because the latter do not work well if facing a large number of
different rates. We demonstrate the practical applicability and efficiency of
the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit
Construction of Polar Codes with Sublinear Complexity
Consider the problem of constructing a polar code of block length for the
transmission over a given channel . Typically this requires to compute the
reliability of all the synthetic channels and then to include those that
are sufficiently reliable. However, we know from [1], [2] that there is a
partial order among the synthetic channels. Hence, it is natural to ask whether
we can exploit it to reduce the computational burden of the construction
problem.
We show that, if we take advantage of the partial order [1], [2], we can
construct a polar code by computing the reliability of roughly a fraction
of the synthetic channels. In particular, we prove that
is a lower bound on the number of synthetic channels to be
considered and such a bound is tight up to a multiplicative factor . This set of roughly synthetic channels is universal, in
the sense that it allows one to construct polar codes for any , and it can
be identified by solving a maximum matching problem on a bipartite graph.
Our proof technique consists of reducing the construction problem to the
problem of computing the maximum cardinality of an antichain for a suitable
partially ordered set. As such, this method is general and it can be used to
further improve the complexity of the construction problem in case a new
partial order on the synthetic channels of polar codes is discovered.Comment: 9 pages, 3 figures, presented at ISIT'17 and submitted to IEEE Trans.
Inform. Theor
Exact Computation of Influence Spread by Binary Decision Diagrams
Evaluating influence spread in social networks is a fundamental procedure to
estimate the word-of-mouth effect in viral marketing. There are enormous
studies about this topic; however, under the standard stochastic cascade
models, the exact computation of influence spread is known to be #P-hard. Thus,
the existing studies have used Monte-Carlo simulation-based approximations to
avoid exact computation.
We propose the first algorithm to compute influence spread exactly under the
independent cascade model. The algorithm first constructs binary decision
diagrams (BDDs) for all possible realizations of influence spread, then
computes influence spread by dynamic programming on the constructed BDDs. To
construct the BDDs efficiently, we designed a new frontier-based search-type
procedure. The constructed BDDs can also be used to solve other
influence-spread related problems, such as random sampling without rejection,
conditional influence spread evaluation, dynamic probability update, and
gradient computation for probability optimization problems.
We conducted computational experiments to evaluate the proposed algorithm.
The algorithm successfully computed influence spread on real-world networks
with a hundred edges in a reasonable time, which is quite impossible by the
naive algorithm. We also conducted an experiment to evaluate the accuracy of
the Monte-Carlo simulation-based approximation by comparing exact influence
spread obtained by the proposed algorithm.Comment: WWW'1
- …