Search results for "computational complexity."
showing 10 items of 245 documents
On the metric properties of dynamic time warping
1987
Recently, some new and promising methods have been proposed to reduce the number of Dynamic Time Warping (DTW) computations in Isolated Word Recognition. For these methods to be properly applicable, the verification of the Triangle Inequality (TI) by the DTW-based Dissimilarity Measure utilized seems to be an important prerequisite.
A polynomial algorithm solving a special class of hybrid optimal control problems
2006
Hybrid optimal control problems are, in general, difficult to solve. A current research goal is to isolate those problems that lead to tractable solutions [5]. In this paper, we identify a special class of hybrid optimal control problems which are easy to solve. We do this by using a paradigm borrowed from the Operations Research field. As main result, we present a solution algorithm that converges to the exact solution in polynomial time. Our approach consists in approximating the hybrid optimal control problem via an integer-linear programming reformulation. The integer-linear programming problem is a Set-covering one with a totally unimodular constraint matrix and therefore solving the S…
A multi-agent system reinforcement learning based optimal power flow for islanded microgrids
2016
In this paper, a distributed intelligence algorithm is used to manage the optimal power flow problem in islanded microgrids. The methodology provides a suboptimal solution although the error is limited to a few percent as compared to a centralized approach. The solution algorithm is multi-agent based. According to the method, couples of agents communicate with each other only if the buses where they are located are electrically connected. The overall prizing system required for learning uses a feedback from an approximated model of the network. Based on the latter, a distributed reiforcement learning algorithm is implemented to minimize the joule losses while meeting operational constraints…
On the effectiveness of Finite Element simulation of orthogonal cutting with particular reference to temperature prediction
2007
Abstract Finite Element simulation of orthogonal cutting is nowadays assuming a large relevance; in fact a very large number of papers may be found out in technical literature on this topic. In recent years, numerical simulation was performed to investigate various phenomena such as chip segmentation, force prediction and tool wear. On the other hand, some drawbacks have to be highlighted; due to the geometrical and computational complexity of the updated-Lagrangian formulation mostly used in FE codes, a cutting time of only a few milliseconds can be effectively simulated. Therefore, steady-state thermal conditions are not reached and the simulation of the thermal phenomenon may be ineffect…
On the Inner Product Predicate and a Generalization of Matching Vector Families
2018
Motivated by cryptographic applications such as predicate encryption, we consider the problem of representing an arbitrary predicate as the inner product predicate on two vectors. Concretely, fix a Boolean function $P$ and some modulus $q$. We are interested in encoding $x$ to $\vec x$ and $y$ to $\vec y$ so that $$P(x,y) = 1 \Longleftrightarrow \langle\vec x,\vec y\rangle= 0 \bmod q,$$ where the vectors should be as short as possible. This problem can also be viewed as a generalization of matching vector families, which corresponds to the equality predicate. Matching vector families have been used in the constructions of Ramsey graphs, private information retrieval (PIR) protocols, and mor…
Combinatorial proofs of two theorems of Lutz and Stull
2021
Recently, Lutz and Stull used methods from algorithmic information theory to prove two new Marstrand-type projection theorems, concerning subsets of Euclidean space which are not assumed to be Borel, or even analytic. One of the theorems states that if $K \subset \mathbb{R}^{n}$ is any set with equal Hausdorff and packing dimensions, then $$ \dim_{\mathrm{H}} π_{e}(K) = \min\{\dim_{\mathrm{H}} K,1\} $$ for almost every $e \in S^{n - 1}$. Here $π_{e}$ stands for orthogonal projection to $\mathrm{span}(e)$. The primary purpose of this paper is to present proofs for Lutz and Stull's projection theorems which do not refer to information theoretic concepts. Instead, they will rely on combinatori…
New separation between $s(f)$ and $bs(f)$
2011
In this note we give a new separation between sensitivity and block sensitivity of Boolean functions: $bs(f)=(2/3)s(f)^2-(1/3)s(f)$.
Adaptive Lower Bound for Testing Monotonicity on the Line
2018
In the property testing model, the task is to distinguish objects possessing some property from the objects that are far from it. One of such properties is monotonicity, when the objects are functions from one poset to another. This is an active area of research. In this paper we study query complexity of $\epsilon$-testing monotonicity of a function $f\colon [n]\to[r]$. All our lower bounds are for adaptive two-sided testers. * We prove a nearly tight lower bound for this problem in terms of $r$. The bound is $\Omega(\frac{\log r}{\log \log r})$ when $\epsilon = 1/2$. No previous satisfactory lower bound in terms of $r$ was known. * We completely characterise query complexity of this probl…
Testing convexity of functions over finite domains
2019
We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains. 1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the upper bound $O(\frac{\log(\epsilon n)}{\epsilon})$ in the usual uniform model, and prove an $O(\frac{\log n}{\epsilon})$ upper bound in the distribution-free setting. 2. We show a tight lower bound of $\Omega(\frac{\log(\epsilon n)}{\epsilon})$ queries for testing convexity of functions $f: [n] \rightarrow \mathbb{R}$ on the line. This lower bound applies to both adaptive and non-adaptive algorithms, and matches the upper bound from item 1, showing that adap…
Sensitivity versus Certificate Complexity of Boolean Functions
2015
Sensitivity, block sensitivity and certificate complexity are basic complexity measures of Boolean functions. The famous sensitivity conjecture claims that sensitivity is polynomially related to block sensitivity. However, it has been notoriously hard to obtain even exponential bounds. Since block sensitivity is known to be polynomially related to certificate complexity, an equivalent of proving this conjecture would be showing that certificate complexity is polynomially related to sensitivity. Previously, it has been shown that $bs(f) \leq C(f) \leq 2^{s(f)-1} s(f) - (s(f)-1)$. In this work, we give a better upper bound of $bs(f) \leq C(f) \leq \max\left(2^{s(f)-1}\left(s(f)-\frac 1 3\righ…