scholarly journals The Complexity of Identifying Large Equivalence Classes

1998 ◽  
Vol 5 (34) ◽  
Author(s):  
Peter G. Binderup ◽  
Gudmund Skovbjerg Frandsen ◽  
Peter Bro Miltersen ◽  
Sven Skyum
Keyword(s):  
Upper Bound ◽  
Equivalence Classes ◽  
Worst Case ◽  
Equivalence Tests

<p>We prove that at least (3k−4) / k(2k−3) n(n-1)/2 − O(k) equivalence tests and no<br />more than 2/k n(n-1)/2 + O(n)<br />equivalence tests are needed in the worst case to identify the equivalence classes with at least k members in set of n elements. The upper bound is an improvement by a factor 2 compared to known results. For k = 3 we give tighter bounds. Finally, for k > n/2 we prove that it is necessary and it suffices to make 2n − k − 1 equivalence tests which generalizes a known result for k = [(n+1)/2] .</p>

scholarly journals Complexity of Nondeterministic Functions

1994 ◽  
Vol 1 (2) ◽  
Author(s):  
Alexander E. Andreev
Keyword(s):  
Upper Bound ◽  
Randomized Algorithms ◽  
Nonempty Intersection ◽  
Linear Size ◽  
Worst Case ◽  
K Value ◽  
Hitting Set ◽  
Set Size

The complexity of a nondeterministic function is the minimum possible complexity of its determinisation. The entropy of a nondeterministic function, F, is minus the logarithm of the ratio between the number of determinisations of F and the number of all deterministic functions.<br /> <br />We obtain an upper bound on the complexity of a nondeterministic function with restricted entropy for the worst case.<br /> <br /> These bounds have strong applications in the problem of algorithm derandomization. A lot of randomized algorithms can be converted to deterministic ones if we have an effective hitting set with certain parameters (a set is hitting for a set system if it has a nonempty intersection with any set from the system).<br /> <br />Linial, Luby, Saks and Zuckerman (1993) constructed the best effective hitting set for the system of k-value, n-dimensional rectangles. The set size is polynomial in k log n / epsilon.<br /> <br />Our bounds of nondeterministic functions complexity offer a possibility to construct an effective hitting set for this system with almost linear size in k log n / epsilon.

scholarly journals Stochastic Flips on Dimer Tilings

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault
Keyword(s):  
Fixed Point ◽  
Markov Process ◽  
Upper Bound ◽  
Numerical Experiments ◽  
Triangular Grid ◽  
Expected Number ◽  
Worst Case ◽  
Average Case ◽  
International Audience

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.

NEW WORST-CASE UPPER BOUND FOR COUNTING EXACT SATISFIABILITY

2014 ◽  
Vol 25 (06) ◽  
pp. 667-678 ◽  
Author(s):  
JUNPING ZHOU ◽  
WEIHUA SU ◽  
JIANAN WANG
Keyword(s):  
Upper Bound ◽  
Worst Case

The counting exact satisfiablity problem (#XSAT) is a problem that computes the number of truth assignments satisfying only one literal in each clause. This paper presents an algorithm that solves the #XSAT problem in O(1.1995n), which is faster than the best algorithm running in O(1.2190n), where n denotes the number of variables. To increase the efficiency of the algorithm, a new principle, called common literals principle, is addressed to simplify formulae. This allows us to further eliminate literals. In addition, we firstly apply the resolution principles into solving #XSAT problem, and therefore it improves the efficiency of the algorithm further.

scholarly journals On Compact Encoding of Pagenumber $k$ Graphs

2008 ◽  
Vol Vol. 10 no. 3 ◽  
Author(s):  
Cyril Gavoille ◽  
Nicolas Hanusse
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Constant Time ◽  
Worst Case ◽  
Encoding Scheme ◽  
Information Theoretic ◽  
Auxiliary Table ◽  
Minimum Number ◽  
International Audience

International audience In this paper we show an information-theoretic lower bound of kn - o(kn) on the minimum number of bits to represent an unlabeled simple connected n-node graph of pagenumber k. This has to be compared with the efficient encoding scheme of Munro and Raman of 2kn + 2m + o(kn+m) bits (m the number of edges), that is 4kn + 2n + o(kn) bits in the worst-case. For m-edge graphs of pagenumber k (with multi-edges and loops), we propose a 2mlog2k + O(m) bits encoding improving the best previous upper bound of Munro and Raman whenever m ≤ 1 / 2kn/log2 k. Actually our scheme applies to k-page embedding containing multi-edge and loops. Moreover, with an auxiliary table of o(m log k) bits, our coding supports (1) the computation of the degree of a node in constant time, (2) adjacency queries with O(logk) queries of type rank, select and match, that is in O(logk *minlogk / loglogm, loglogk) time and (3) the access to δ neighbors in O(δ) runs of select, rank or match;.

scholarly journals Nano topology induced by Lattices

2019 ◽  
Vol 38 (5) ◽  
pp. 197-204
Author(s):  
M. Lellis Thivagar ◽  
V. Sutha Devi
Keyword(s):  
Lower Bound ◽  
19Th Century ◽  
Upper Bound ◽  
Lattice Theory ◽  
Ordered Set ◽  
Equivalence Classes ◽  
The Other ◽  
Five Elements ◽  
Lower And Upper Approximations ◽  
The 19Th Century

Lattice is a partially ordered set in which all finite subsets have a least upper bound and greatest lower bound. Dedekind worked on lattice theory in the 19th century. Nano topology explored by Lellis Thivagar et.al. can be described as a collection of nano approximations, a non-empty finite universe and empty set for which equivalence classes are buliding blocks. This is named as Nano topology, because of its size and what ever may be the size of universe it has atmost five elements in it. The elements of Nano topology are called the Nano open sets. This paper is to study the nano topology within the context of lattices. In lattice, there is a special class of joincongruence relation which is defined with respect to an ideal. We have defined the nano approximations of a set with respect to an ideal of a lattice. Also some properties of the approximations of a set in a lattice with respect to ideals are studied. On the other hand, the lower and upper approximations have also been studied within the context various algebraic structures.

Risk assessment of chronic dietary exposure to the conjugated mycotoxin deoxynivalenol-3-β-glucoside in the Dutch population

2015 ◽  
Vol 8 (5) ◽  
pp. 561-572 ◽  
Author(s):  
E.M. Janssen ◽  
R.C. Sprong ◽  
P.W. Wester ◽  
M. De Boevre ◽  
M.J.B. Mengelers
Keyword(s):  
Risk Assessment ◽  
Body Weight ◽  
The Netherlands ◽  
Food Consumption ◽  
Upper Bound ◽  
Chronic Exposure ◽  
Dietary Exposure ◽  
Food Products ◽  
Dutch Population ◽  
Worst Case

In this study, a risk assessment of dietary exposure to the conjugated mycotoxin deoxynivalenol-3-β-glucoside (DON-3G) in the Dutch population was conducted. Data on DON-3G levels in food products available in the Netherlands are scarce. Therefore, data on co-occurring levels of DON-3G and deoxynivalenol (DON), its parent compound, were used to estimate the DON-3G/DON ratio for several food product categories. This resulted in a DON-3G/DON ratio of 0.2 (90% confidence interval (CI): 0.04-0.9) in grains & grain-milling products, 0.3 (90% CI: 0.03-2.8) in grain-based products and 0.8 (90% CI: 0.4-1.8) in beer. These ratios were applied to the Dutch monitoring data of DON to estimate the DON-3G concentrations in food products available in the Netherlands. DON and DON-3G concentrations were combined with food consumption data of two Dutch National Food Consumption Surveys to assess chronic exposure in young children (2-6 years), children (7-16 years) and adults (17-69 years) using the Monte Carlo Risk Assessment program. The chronic exposure levels of DON, DON-3G and the sum of both compounds (DON+DON-3G) were compared to the tolerable daily intake (TDI) of 1 μg/kg body weight/day which is based on the most critical effect of DON, namely decreased body weight gain. The assumption was made that DON-3G is deconjugated and then fully absorbed as DON in the gastro-intestinal tract. Exposure (P97.5) of the population aged 7-16 years and 17-69 years to DON or DON-3G separately, did not exceed the TDI. However, exposure to upper bound levels of DON+DON-3G (i.e. worst-case scenario) in the same age categories (P97.5) exceeded the TDI with a maximum factor of 1.3. Exposure (P97.5) of the 2-6 year-olds to DON was close to the TDI. Within this group, exposure (P97.5) to upper bound levels of DON+DON-3G exceeded the TDI with not more than a factor 2.

scholarly journals On the Largest Dynamic Monopolies of Graphs with a Given Average Threshold

2015 ◽  
Vol 58 (2) ◽  
pp. 306-316 ◽  
Author(s):  
Kaveh Khoshkhah ◽  
Manouchehr Zaker
Keyword(s):  
Polynomial Time ◽  
Upper Bound ◽  
Nonnegative Integer ◽  
Planar Graphs ◽  
Worst Case ◽  
Time Solution

AbstractLet G be a graph and let τ be an assignment of nonnegative integer thresholds to the vertices of G. A subset of vertices, D, is said to be a τ-dynamicmonopoly if V(G) can be partitioned into subsets D0 , D1, …, Dk such that D0 = D and for any i ∊ {0, . . . , k−1}, each vertex v in Di+1 has at least τ(v) neighbors in D0∪··· ∪Di. Denote the size of smallest τ-dynamicmonopoly by dynτ(G) and the average of thresholds in τ by τ. We show that the values of dynτ(G) over all assignments τ with the same average threshold is a continuous set of integers. For any positive number t, denote the maximum dynτ(G) taken over all threshold assignments τ with τ ≤ t, by Ldynt(G). In fact, Ldynt(G) shows the worst-case value of a dynamicmonopoly when the average threshold is a given number t. We investigate under what conditions on t, there exists an upper bound for Ldynt(G) of the form c|G|, where c < 1. Next, we show that Ldynt(G) is coNP-hard for planar graphs but has polynomial-time solution for forests.

scholarly journals Roundness: A closed form upper bound for the centroid to minimum zone center distance by worst-case analysis

Measurement ◽  
2013 ◽  
Vol 46 (7) ◽  
pp. 2251-2258 ◽  
Author(s):  
Andrea Rossi ◽  
Michele Lanzetta
Keyword(s):  
Closed Form ◽  
Upper Bound ◽  
Case Analysis ◽  
Worst Case Analysis ◽  
Worst Case ◽  
Minimum Zone ◽  
Center Distance
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