Search results for "Log-log plot"
showing 5 items of 5 documents
Fast Algorithms for Pseudoarboricity
2015
The densest subgraph problem, which asks for a subgraph with the maximum edges-to-vertices ratio d∗, is solvable in polynomial time. We discuss algorithms for this problem and the computation of a graph orientation with the lowest maximum indegree, which is equal to ⌈d∗⌉. This value also equals the pseudoarboricity of the graph. We show that it can be computed in O(|E| √ log log d∗) time, and that better estimates can be given for graph classes where d∗ satisfies certain asymptotic bounds. These runtimes are achieved by accelerating a binary search with an approximation scheme, and a runtime analysis of Dinitz’s algorithm on flow networks where all arcs, except the source and sink arcs, hav…
Quantum Identification of Boolean Oracles
2004
The oracle identification problem (OIP) is, given a set S of M Boolean oracles out of 2 N ones, to determine which oracle in S is the current black-box oracle. We can exploit the information that candidates of the current oracle is restricted to S. The OIP contains several concrete problems such as the original Grover search and the Bernstein-Vazirani problem. Our interest is in the quantum query complexity, for which we present several upper bounds. They are quite general and mostly optimal: (i) The query complexity of OIP is \(O(\sqrt{N {\rm log} M {\rm log} N}{\rm log log} M)\) for anyS such that M = |S| > N, which is better than the obvious bound N if M \(< 2^{N/log^3 N}\). (ii) It is \…
Tally languages accepted by alternating multitape finite automata
1997
We consider k-tape 1-way alternating finite automata (k-tape lafa). We say that an alternating automaton accepts a language L\(\subseteq\)(Σ*)k with f(n)-bounded maximal (respectively, minimal) leaf-size if arbitrary (respectively, at least one) accepting tree for any (w1, w2,..., wk) ∈ L has no more than $$f\mathop {(\max }\limits_{1 \leqslant i \leqslant k} \left| {w_i } \right|)$$ leaves. The main results of the paper are the following. If k-tape lafa accepts language L over one-letter alphabet with o(log n)-bounded maximal leaf-size or o(log log n)-bounded minimal leaf-size then the language L is semilinear. Moreover, if a language L is accepted with o(log log(n))-bounded minimal (respe…
The rightmost equal-cost position problem.
2013
LZ77-based compression schemes compress the input text by replacing factors in the text with an encoded reference to a previous occurrence formed by the couple (length, offset). For a given factor, the smallest is the offset, the smallest is the resulting compression ratio. This is optimally achieved by using the rightmost occurrence of a factor in the previous text. Given a cost function, for instance the minimum number of bits used to represent an integer, we define the Rightmost Equal-Cost Position (REP) problem as the problem of finding one of the occurrences of a factor whose cost is equal to the cost of the rightmost one. We present the Multi-Layer Suffix Tree data structure that, for…
Stability of the Calderón problem in admissible geometries
2014
In this paper we prove log log type stability estimates for inverse boundary value problems on admissible Riemannian manifolds of dimension n ≥ 3. The stability estimates correspond to the uniqueness results in [13]. These inverse problems arise naturally when studying the anisotropic Calderon problem. peerReviewed