8,511 research outputs found
Solution of Optimal Power Flow Problems using Moment Relaxations Augmented with Objective Function Penalization
The optimal power flow (OPF) problem minimizes the operating cost of an
electric power system. Applications of convex relaxation techniques to the
non-convex OPF problem have been of recent interest, including work using the
Lasserre hierarchy of "moment" relaxations to globally solve many OPF problems.
By preprocessing the network model to eliminate low-impedance lines, this paper
demonstrates the capability of the moment relaxations to globally solve large
OPF problems that minimize active power losses for portions of several European
power systems. Large problems with more general objective functions have thus
far been computationally intractable for current formulations of the moment
relaxations. To overcome this limitation, this paper proposes the combination
of an objective function penalization with the moment relaxations. This
combination yields feasible points with objective function values that are
close to the global optimum of several large OPF problems. Compared to an
existing penalization method, the combination of penalization and the moment
relaxations eliminates the need to specify one of the penalty parameters and
solves a broader class of problems.Comment: 8 pages, 1 figure, to appear in IEEE 54th Annual Conference on
Decision and Control (CDC), 15-18 December 201
Limits of Preprocessing
We present a first theoretical analysis of the power of polynomial-time
preprocessing for important combinatorial problems from various areas in AI. We
consider problems from Constraint Satisfaction, Global Constraints,
Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a
complexity theoretic assumption, none of the considered problems can be reduced
by polynomial-time preprocessing to a problem kernel whose size is polynomial
in a structural problem parameter of the input, such as induced width or
backdoor size. Our results provide a firm theoretical boundary for the
performance of polynomial-time preprocessing algorithms for the considered
problems.Comment: This is a slightly longer version of a paper that appeared in the
proceedings of AAAI 201
Guarantees and Limits of Preprocessing in Constraint Satisfaction and Reasoning
We present a first theoretical analysis of the power of polynomial-time
preprocessing for important combinatorial problems from various areas in AI. We
consider problems from Constraint Satisfaction, Global Constraints,
Satisfiability, Nonmonotonic and Bayesian Reasoning under structural
restrictions. All these problems involve two tasks: (i) identifying the
structure in the input as required by the restriction, and (ii) using the
identified structure to solve the reasoning task efficiently. We show that for
most of the considered problems, task (i) admits a polynomial-time
preprocessing to a problem kernel whose size is polynomial in a structural
problem parameter of the input, in contrast to task (ii) which does not admit
such a reduction to a problem kernel of polynomial size, subject to a
complexity theoretic assumption. As a notable exception we show that the
consistency problem for the AtMost-NValue constraint admits a polynomial kernel
consisting of a quadratic number of variables and domain values. Our results
provide a firm worst-case guarantees and theoretical boundaries for the
performance of polynomial-time preprocessing algorithms for the considered
problems.Comment: arXiv admin note: substantial text overlap with arXiv:1104.2541,
arXiv:1104.556
Tractable Pathfinding for the Stochastic On-Time Arrival Problem
We present a new and more efficient technique for computing the route that
maximizes the probability of on-time arrival in stochastic networks, also known
as the path-based stochastic on-time arrival (SOTA) problem. Our primary
contribution is a pathfinding algorithm that uses the solution to the
policy-based SOTA problem---which is of pseudo-polynomial-time complexity in
the time budget of the journey---as a search heuristic for the optimal path. In
particular, we show that this heuristic can be exceptionally efficient in
practice, effectively making it possible to solve the path-based SOTA problem
as quickly as the policy-based SOTA problem. Our secondary contribution is the
extension of policy-based preprocessing to path-based preprocessing for the
SOTA problem. In the process, we also introduce Arc-Potentials, a more
efficient generalization of Stochastic Arc-Flags that can be used for both
policy- and path-based SOTA. After developing the pathfinding and preprocessing
algorithms, we evaluate their performance on two different real-world networks.
To the best of our knowledge, these techniques provide the most efficient
computation strategy for the path-based SOTA problem for general probability
distributions, both with and without preprocessing.Comment: Submission accepted by the International Symposium on Experimental
Algorithms 2016 and published by Springer in the Lecture Notes in Computer
Science series on June 1, 2016. Includes typographical corrections and
modifications to pre-processing made after the initial submission to SODA'15
(July 7, 2014
The size of BDDs and other data structures in temporal logics model checking
Temporal Logic Model Checking is a verification method in which we describe a system, the model, and then we verify whether important properties, expressed in a temporal logic formula, hold in the system. Many Model Checking tools employ BDDs or some other data structure to represent sets of states. It has been empirically observed that the BDDs used in these algorithms may grow exponentially as the model and formula increase in size. We formally prove that no kind of data structure of polynomial size can represent the set of valid initial states for all models and all formulae. This result holds for all data structures where a state can be checked in polynomial time. Therefore, it holds not only for all types of BDDs regardless of variable ordering, but also for more powerful data structures, such as RBCs, MTBDDs, ADDs and SDDs. Thus, the size explosion of BDDs is not a limit of these specific data representation structures, but is unavoidable: every formalism used in the same way would lead to an exponential size blow up
Stochastic Divergence Minimization for Biterm Topic Model
As the emergence and the thriving development of social networks, a huge
number of short texts are accumulated and need to be processed. Inferring
latent topics of collected short texts is useful for understanding its hidden
structure and predicting new contents. Unlike conventional topic models such as
latent Dirichlet allocation (LDA), a biterm topic model (BTM) was recently
proposed for short texts to overcome the sparseness of document-level word
co-occurrences by directly modeling the generation process of word pairs.
Stochastic inference algorithms based on collapsed Gibbs sampling (CGS) and
collapsed variational inference have been proposed for BTM. However, they
either require large computational complexity, or rely on very crude
estimation. In this work, we develop a stochastic divergence minimization
inference algorithm for BTM to estimate latent topics more accurately in a
scalable way. Experiments demonstrate the superiority of our proposed algorithm
compared with existing inference algorithms.Comment: 19 pages, 4 figure
On the Complexity of Case-Based Planning
We analyze the computational complexity of problems related to case-based
planning: planning when a plan for a similar instance is known, and planning
from a library of plans. We prove that planning from a single case has the same
complexity than generative planning (i.e., planning "from scratch"); using an
extended definition of cases, complexity is reduced if the domain stored in the
case is similar to the one to search plans for. Planning from a library of
cases is shown to have the same complexity. In both cases, the complexity of
planning remains, in the worst case, PSPACE-complete
Making Queries Tractable on Big Data with Preprocessing
A query class is traditionally considered tractable if there exists a polynomial-time (PTIME) algorithm to answer its queries. When it comes to big data, however, PTIME al-gorithms often become infeasible in practice. A traditional and effective approach to coping with this is to preprocess data off-line, so that queries in the class can be subsequently evaluated on the data efficiently. This paper aims to pro-vide a formal foundation for this approach in terms of com-putational complexity. (1) We propose a set of Î -tractable queries, denoted by Î T0Q, to characterize classes of queries that can be answered in parallel poly-logarithmic time (NC) after PTIME preprocessing. (2) We show that several natu-ral query classes are Î -tractable and are feasible on big data. (3) We also study a set Î TQ of query classes that can be ef-fectively converted to Î -tractable queries by re-factorizing its data and queries for preprocessing. We introduce a form of NC reductions to characterize such conversions. (4) We show that a natural query class is complete for Î TQ. (5) We also show that Î T0Q â P unless P = NC, i.e., the set Î T0Q of all Î -tractable queries is properly contained in the set P of all PTIME queries. Nonetheless, Î TQ = P, i.e., all PTIME query classes can be made Î -tractable via proper re-factorizations. This work is a step towards understanding the tractability of queries in the context of big data. 1
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