Almost Safe Group Testing with Few Tests

1994 ◽  
Vol 3 (3) ◽  
pp. 411-419
Author(s):  
Andrzej Pelc
Keyword(s):  
Lower Bounds ◽  
Group Testing ◽  
Upper And Lower Bounds ◽  
Probability Functions ◽  
Minimum Number ◽  
Location Strategies

In group testing, sets of data undergo tests that reveal if a set contains faulty data. Assuming that data items are faulty with given probability and independently of one another, we investigate small families of tests that enable us to locate correctly all faulty data with probability converging to one as the amount of data grows. Upper and lower bounds on the minimum number of such tests are established for different probability functions, and respective location strategies are constructed.

2-Distance chromatic number of some graph products

2020 ◽  
Vol 12 (02) ◽  
pp. 2050021
Author(s):  
Ghazale Ghazi ◽  
Freydoon Rahbarnia ◽  
Mostafa Tavakoli
Keyword(s):  
Chromatic Number ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Graph Products ◽  
Lexicographic Product ◽  
Graph Product ◽  
Minimum Number

This paper studies the 2-distance chromatic number of some graph product. A coloring of [Formula: see text] is 2-distance if any two vertices at distance at most two from each other get different colors. The minimum number of colors in the 2-distance coloring of [Formula: see text] is the 2-distance chromatic number and denoted by [Formula: see text]. In this paper, we obtain some upper and lower bounds for the 2-distance chromatic number of the rooted product, generalized rooted product, hierarchical product and we determine exact value for the 2-distance chromatic number of the lexicographic product.

The Thickness of the Cartesian Product of Two Graphs

2016 ◽  
Vol 59 (4) ◽  
pp. 705-720
Author(s):  
Yichao Chen ◽  
Xuluo Yin
Keyword(s):  
Lower Bounds ◽  
Planar Graphs ◽  
Complete Bipartite Graph ◽  
Cartesian Product ◽  
Upper And Lower Bounds ◽  
Minimal Graph ◽  
Minimum Number ◽  
Complete Bipartite Graphs ◽  
Planar Subgraphs ◽  
Proper Subgraph

AbstractThe thickness of a graph G is the minimum number of planar subgraphs whose union is G. A t-minimal graph is a graph of thickness t that contains no proper subgraph of thickness t. In this paper, upper and lower bounds are obtained for the thickness, t(G ⎕ H), of the Cartesian product of two graphs G and H, in terms of the thickness t(G) and t(H). Furthermore, the thickness of the Cartesian product of two planar graphs and of a t-minimal graph and a planar graph are determined. By using a new planar decomposition of the complete bipartite graph K4k,4k, the thickness of the Cartesian product of two complete bipartite graphs Kn,n and Kn,n is also given for n≠4k + 1.

COVERING A SET OF POINTS WITH A MINIMUM NUMBER OF TURNS

2004 ◽  
Vol 14 (01n02) ◽  
pp. 105-114 ◽  
Author(s):  
MICHAEL J. COLLINS
Keyword(s):  
Euclidean Space ◽  
Lower Bounds ◽  
Piecewise Linear ◽  
Upper And Lower Bounds ◽  
Linear Path ◽  
Change Direction ◽  
Finite Set ◽  
Minimum Number ◽  
Pass Through ◽  
Set Of Points

Given a finite set of points in Euclidean space, we can ask what is the minimum number of times a piecewise-linear path must change direction in order to pass through all of them. We prove some new upper and lower bounds for the rectilinear version of this problem in which all motion is orthogonal to the coordinate axes. We also consider the more general case of arbitrary directions.

scholarly journals Minimum survivable graphs with bounded distance increase

2003 ◽  
Vol Vol. 6 no. 1 ◽  
Author(s):  
Selma Djelloul ◽  
Mekkia Kouider
Keyword(s):  
Fault Tolerance ◽  
Lower Bounds ◽  
Interconnection Networks ◽  
Negative Integer ◽  
Upper And Lower Bounds ◽  
Minimum Size ◽  
Np Hard ◽  
Bounded Distance ◽  
Minimum Number ◽  
International Audience

International audience We study in graphs properties related to fault-tolerance in case a node fails. A graph G is k-self-repairing, where k is a non-negative integer, if after the removal of any vertex no distance in the surviving graph increases by more than k. In the design of interconnection networks such graphs guarantee good fault-tolerance properties. We give upper and lower bounds on the minimum number of edges of a k-self-repairing graph for prescribed k and n, where n is the order of the graph. We prove that the problem of finding, in a k-self-repairing graph, a spanning k-self-repairing subgraph of minimum size is NP-Hard.

Representation of permutations as products of cycles of fixed length

1976 ◽  
Vol 22 (3) ◽  
pp. 321-331 ◽  
Author(s):  
Marcel Herzog ◽  
K. B. Reid
Keyword(s):  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Exact Results ◽  
Fixed Length ◽  
Minimum Number

AbstractWe study the problem of representing a permutation C as a product of a minimum number, fk(C), of cycles of length k. Upper and lower bounds on fk(C) are obtained and exact results are derived for k = 2, 3, 4.

scholarly journals Theoretical Bounds on Performance in Threshold Group Testing Schemes

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 637
Author(s):  
Jin-Taek Seong
Keyword(s):  
Channel Coding ◽  
Coding Theory ◽  
Large Population ◽  
Group Testing ◽  
Density Ratio ◽  
Upper And Lower Bounds ◽  
Probability Of Error ◽  
Group Matrix ◽  
Minimum Number ◽  
Threshold Group Testing

A threshold group testing (TGT) scheme with lower and upper thresholds is a general model of group testing (GT) which identifies a small set of defective samples. In this paper, we consider the TGT scheme that require the minimum number of tests. We aim to find lower and upper bounds for finding a set of defective samples in a large population. The decoding for the TGT scheme is exploited by minimization of the Hamming weight in channel coding theory and the probability of error is also defined. Then, we derive a new upper bound on the probability of error and extend a lower bound from conventional one to the TGT scheme. We show that the upper and lower bounds well match with each other at the optimal density ratio of the group matrix. In addition, we conclude that when the gaps between the two thresholds in the TGT framework increase, the group matrix with a high density should be used to achieve optimal performance.

scholarly journals TRIPLE CROSSING NUMBER OF KNOTS AND LINKS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350006 ◽  
Author(s):  
COLIN ADAMS
Keyword(s):  
Lower Bounds ◽  
Crossing Number ◽  
Upper And Lower Bounds ◽  
Minimum Number ◽  
Bracket Polynomial ◽  
Knots And Links

A triple crossing is a crossing in a projection of a knot or link that has three strands of the knot passing straight through it. A triple crossing projection is a projection such that all of the crossings are triple crossings. We prove that every knot and link has a triple crossing projection and then investigate c3(K), which is the minimum number of triple crossings in a projection of K. We obtain upper and lower bounds on c3(K) in terms of the traditional crossing number and show that both are realized. We also relate triple crossing number to the span of the bracket polynomial and use this to determine c3(K) for a variety of knots and links. We then use c3(K) to obtain bounds on the volume of a hyperbolic knot or link. We also consider extensions to cn(K).

scholarly journals Injective edge coloring of graphs

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6411-6423
Author(s):  
Domingos Cardoso ◽  
Orestes Cerdeira ◽  
Charles Dominicc ◽  
Pedro Cruz
Keyword(s):  
Lower Bounds ◽  
Edge Coloring ◽  
Upper And Lower Bounds ◽  
Coloring Number ◽  
Minimum Number ◽  
Np Complete

Three edges e1, e2 and e3 in a graph G are consecutive if they form a path (in this order) or a cycle of lengths three. An injective edge coloring of a graph G = (V, E) is a coloring c of the edges of G such that if e1, e2 and e3 are consecutive edges in G, then c(e1)? c(e3). The injective edge coloring number ?'i(G) is the minimum number of colors permitted in such a coloring. In this paper, exact values of ?'i(G) for several classes of graphs are obtained, upper and lower bounds for ?'i(G) are introduced and it is proven that checking whether ?'i(G) = k is NP-complete.

scholarly journals ON THE NUMBER OF RATIONAL POINTS ON PRYM VARIETIES OVER FINITE FIELDS

2015 ◽  
Vol 58 (1) ◽  
pp. 55-68 ◽  
Author(s):  
YVES AUBRY ◽  
SAFIA HALOUI
Keyword(s):  
Finite Fields ◽  
Lower Bounds ◽  
Rational Points ◽  
Upper And Lower Bounds ◽  
Prym Varieties ◽  
Minimum Number ◽  
Dimension 2

AbstractWe give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.

scholarly journals Analytic Study of Complex Fractional Tsallis’ Entropy with Applications in CNNs

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 722 ◽  
Author(s):  
Rabha Ibrahim ◽  
Maslina Darus
Keyword(s):  
Neural Networks ◽  
Lower Bounds ◽  
Special Functions ◽  
Tsallis Entropy ◽  
Analytic Study ◽  
Complex Domain ◽  
Upper And Lower Bounds ◽  
Probability Functions ◽  
Fractional Entropy ◽  
Definition Of

In this paper, we study Tsallis’ fractional entropy (TFE) in a complex domain by applying the definition of the complex probability functions. We study the upper and lower bounds of TFE based on some special functions. Moreover, applications in complex neural networks (CNNs) are illustrated to recognize the accuracy of CNNs.

Sign in / Sign up

Export Citation Format

Share Document