Related papers: A Generalized Worst-Case Complexity Analysis for N…
In this survey, we address the worst-case, average-case, and generic-case time complexity of the word problem and some other algorithmic problems in several classes of groups and show that it is often the case that the average-case…
In this paper, we study the communication complexity for the problem of computing a conjunctive query on a large database in a parallel setting with $p$ servers. In contrast to previous work, where upper and lower bounds on the…
The problem of minimizing a multilinear function of binary variables is a well-studied NP-hard problem. The set of solutions of the standard linearization of this problem is called the multilinear set. We study a cardinality constrained…
Linear complexity is an important parameter for arrays that are used in applications related to information security. In this work we survey constructions of two and three dimensional arrays, and present new results on the multidimensional…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
We investigate the searchability of complex systems in terms of their interconnectedness. Associating searchability with the number and size of branch points along the paths between the nodes, we find that scale-free networks are relatively…
We describe a new algorithm, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, `beyond worst-case guarantees') for data in indexed search trees. Our first contribution is…
We systematically investigate the complexity of model checking the existential positive fragment of first-order logic. In particular, for a set of existential positive sentences, we consider model checking where the sentence is restricted…
We introduce and discuss the notion of monotonicity for the complexity measures of general probability distributions, patterned after the resource theory of quantum entanglement. Then, we explore whether this property is satisfied by the…
In this paper we study the complexity of the motion planning problem for control-affine systems. Such complexities are already defined and rather well-understood in the particular case of nonholonomic (or sub-Riemannian) systems. Our aim is…
This paper investigates fuzzy nonlinear system equations using an optimization approach. Here, the inner-outer direct search technique is used with fuzzy coefficients and vectors to quantify the uncertain solution. The fuzzy nonlinear…
Within the framework of generalized combinatorial approach, the complexity is determined for infinite set of self-similar hierarchical ensembles. This complexity is shown to increase with strengthening of the hierarchy coupling to the…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
One-max search is a classic problem in online decision-making, in which a trader acts on a sequence of revealed prices and accepts one of them irrevocably to maximise its profit. The problem has been studied both in probabilistic and in…
Given a dynamical system with constrained outputs, the maximal admissible set (MAS) is defined as the set of all initial conditions such that the output constraints are satisfied for all time. It has been previously shown that for…
We examine optimization problems in which an investor has the opportunity to trade in $d$ stocks with the goal of maximizing her worst-case cost of cumulative gains and losses. Here, worst-case refers to taking into account all possible…
While various complexity measures for deep neural networks exist, specifying an appropriate measure capable of predicting and explaining generalization in deep networks has proven challenging. We propose Neural Complexity (NC), a…
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as an optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic…
Gradient-free/zeroth-order methods for black-box convex optimization have been extensively studied in the last decade with the main focus on oracle calls complexity. In this paper, besides the oracle complexity, we focus also on iteration…