Search results for "Complexity"
showing 10 items of 1094 documents
The computational complexity of the relative robust shortest path problem with interval data
2004
Abstract The paper deals with the relative robust shortest path problem in a directed arc weighted graph, where arc lengths are specified as intervals containing possible realizations of arc lengths. The complexity status of this problem has been unknown in the literature. We show that the problem is NP -hard.
The computational complexity of the criticality problems in a network with interval activity times
2002
Abstract The paper analyzes the criticality in a network with interval activities duration times. A natural generalization of the criticality notion (for a path, an activity and an event) for the case of network with interval activity duration times is given. The computation complexity of five problems linked to the introduced criticality notion is presented.
Periodicity and repetitions in parameterized strings
2008
AbstractOne of the most beautiful and useful notions in the Mathematical Theory of Strings is that of a Period, i.e., an initial piece of a given string that can generate that string by repeating itself at regular intervals. Periods have an elegant mathematical structure and a wealth of applications [F. Mignosi and A. Restivo, Periodicity, Algebraic Combinatorics on Words, in: M. Lothaire (Ed.), Cambridge University Press, Cambridge, pp. 237–274, 2002]. At the hearth of their theory, there are two Periodicity Lemmas: one due to Lyndon and Schutzenberger [The equation aM=bNcP in a free group, Michigan Math. J. 9 (1962) 289–298], referred to as the Weak Version, and the other due to Fine and …
Quantum Finite Automata and Logics
2006
The connection between measure once quantum finite automata (MO-QFA) and logic is studied in this paper. The language class recognized by MO-QFA is compared to languages described by the first order logics and modular logics. And the equivalence between languages accepted by MO-QFA and languages described by formulas using Lindstrom quantifier is shown.
Logics with counting and equivalence
2014
We consider the two-variable fragment of first-order logic with counting, subject to the stipulation that a single distinguished binary predicate be interpreted as an equivalence. We show that the satisfiability and finite satisfiability problems for this logic are both NEXPTIME-complete. We further show that the corresponding problems for two-variable first-order logic with counting and two equivalences are both undecidable.
Minimal Morse flows on compact manifolds
2006
Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.
Quantum Algorithms for Learning Symmetric Juntas via Adversary Bound
2014
In this paper, we study the following variant of the junta learning problem. We are given oracle access to a Boolean function f on n variables that only depends on k variables, and, when restricted to them, equals some predefined function h. The task is to identify the variables the function depends on. This is a generalisation of the Bernstein-Vazirani problem (when h is the XOR function) and the combinatorial group testing problem (when h is the OR function). We analyse the general case using the adversary bound, and give an alternative formulation for the quantum query complexity of this problem. We construct optimal quantum query algorithms for the cases when h is the OR function (compl…
Time-Efficient Quantum Walks for 3-Distinctness
2013
We present two quantum walk algorithms for 3-Distinctness. Both algorithms have time complexity $\tilde{O}(n^{5/7})$, improving the previous $\tilde{O}(n^{3/4})$ and matching the best known upper bound for query complexity (obtained via learning graphs) up to log factors. The first algorithm is based on a connection between quantum walks and electric networks. The second algorithm uses an extension of the quantum walk search framework that facilitates quantum walks with nested updates.
Balls into non-uniform bins
2014
Balls-into-bins games for uniform bins are widely used to model randomized load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-to-peer (P2P) networks, which are not able to perfectly balance the load over the bins. While previous evaluations try to find strategies for uniform bins under non-uniform bin selection probabilities, this paper investigates heterogeneous bins, where the "capacities" of the bins might differ significantly. We show that heterogeneous environments can even help to distribute the load more eve…
A multilinear Phelps' Lemma
2007
We prove a multilinear version of Phelps' Lemma: if the zero sets of multilinear forms of norm one are 'close', then so are the multilinear forms.