scholarly journals On the Cycle Augmentation Problem: Hardness and Approximation Algorithms

2021 ◽  
Author(s):  
Waldo Gálvez ◽  
Fabrizio Grandoni ◽  
Afrouz Jabal Ameli ◽  
Krzysztof Sornat
Keyword(s):  
Approximation Algorithms ◽  
Connected Graph ◽  
Minimum Size ◽  
Single Cycle ◽  
Integrality Gap ◽  
Connectivity Augmentation ◽  
Special Case ◽  
Better Than

AbstractIn the k-Connectivity Augmentation Problem we are given a k-edge-connected graph and a set of additional edges called links. Our goal is to find a set of links of minimum size whose addition to the graph makes it (k + 1)-edge-connected. There is an approximation preserving reduction from the mentioned problem to the case k = 1 (a.k.a. the Tree Augmentation Problem or TAP) or k = 2 (a.k.a. the Cactus Augmentation Problem or CacAP). While several better-than-2 approximation algorithms are known for TAP, for CacAP only recently this barrier was breached (hence for k-Connectivity Augmentation in general). As a first step towards better approximation algorithms for CacAP, we consider the special case where the input cactus consists of a single cycle, the Cycle Augmentation Problem (CycAP). This apparently simple special case retains part of the hardness of the general case. In particular, we are able to show that it is APX-hard. In this paper we present a combinatorial $\left (\frac {3}{2}+\varepsilon \right )$ 3 2 + ε -approximation for CycAP, for any constant ε > 0. We also present an LP formulation with a matching integrality gap: this might be useful to address the general case of the problem.

Transplantation of coral fragment, Acropora formosa (Scleractinia)

2014 ◽  
pp. 1
Author(s):  
Hanny Tioho ◽  
Maykel A.J Karauwan
Keyword(s):  
Fragment Size ◽  
Observation Time ◽  
Minimum Size ◽  
Average Growth Rate ◽  
Average Growth ◽  
Significant Difference ◽  
Acropora Formosa ◽  
Survival And Growth ◽  
One Way Anova ◽  
Better Than

The minimum size of coral transplants, Acropora formosa, was assessed to support their survival and growth. For this, 150 coral fragments of different sizes (5, 10, 15 cm) were transplanted close to the donor colony. Their survivorship and growth were observed for 12 months. At the end of the observation time, 90% of 15 cm-transplanted coral fragments survived, while the others (10cm and 5 cm) did 86% and 82% respectively. The average growth rate of 5 cm-coral fragments was 0.860 cm/month, while 10 and 15 cm-fragments were 0.984 cm/month and 1.108 cm/month respectively. One-way ANOVA showed that there was significant difference (p<0.05) among the three (5, 10, 15 cm) transplant initial sizes in which the longest fragment size tended to survive longer than the smaller one.  However, the smaller transplants grew better than the bigger one, 10.318 cm/year (206%) for 5 cm-transplant, 11.803 cm/year (118%) for 10 cm-transplant, and 13.299 cm/year (89%) for 15 cm-transplant, respectively. Ukuran minimal fragmen karang Acropora formosa yang ditransplantasi diduga untuk mendukung ketahanan hidup dan pertumbuhannya. Untuk itu, 150 fragmen karang ditransplantasi ke lokasi yang berdekatan dengan koloni induknya.  Ketahanan hidup dan pertumbuhan semua fragmen karang yang ditransplantasi diamati selama 12 bulan.  Pada akhir pengamatan, 90% dari fragmen karang berukuran 15 cm yang ditransplantasi dapat bertahan hidup, sedangkan yang lainnya (ukuran 10 cm dan 5 cm) masing-masing sebesar 86% dan 82%.  Rata-rata laju pertumbuhan fragmen karang dengan ukuran awal 5 cm adalah 0,860 cm/bulan, sedangkan ukuran fragmen 10 dan 15 cm masing-masing adalah 0,984 cm/bulan and 1,108 cm/bulan. ANOVA satu arah menunjukkan adanya perbedaan yang nyata (p<0.05) antara ketiga ukuran fragmen yang berbeda, di mana ukuran fragmen karang yang lebih panjang cenderung mempunyai ketahanan hidup yang lebih baik. Namun demikian, ukuran transplant yang lebih kecil memiliki pertumbuhan lebih baik dibandingkan dengan ukuran yang lebih besar, yakni10,318 cm/tahun (206%) untuk transplant berukuran 5 cm, 11,803 cm/tahun (118%) untuk 10 cm, dan 13,299 cm/tahun (89%) untuk ukuran 15 cm.

COMPUTING THE RUPTURE DEGREE IN COMPOSITE GRAPHS

2010 ◽  
Vol 21 (03) ◽  
pp. 311-319 ◽  
Author(s):  
AYSUN AYTAC ◽  
ZEYNEP NIHAN ODABAS
Keyword(s):  
Complete Graph ◽  
Connected Graph ◽  
The Other ◽  
Trade Off ◽  
Number Of Components ◽  
Np Complete ◽  
Work Done ◽  
Better Than

The rupture degree of an incomplete connected graph G is defined by [Formula: see text] where w(G - S) is the number of components of G - S and m(G - S) is the order of a largest component of G - S. For the complete graph Kn, rupture degree is defined as 1 - n. This parameter can be used to measure the vulnerability of a graph. Rupture degree can reflect the vulnerability of graphs better than or independent of the other parameters. To some extent, it represents a trade-off between the amount of work done to damage the network and how badly the network is damaged. Computing the rupture degree of a graph is NP-complete. In this paper, we give formulas for the rupture degree of composition of some special graphs and we consider the relationships between the rupture degree and other vulnerability parameters.

Modeling of Nonlinear Viscoelastic Creep of Polycarbonate

e-Polymers ◽  
2007 ◽  
Vol 7 (1) ◽  
Author(s):  
Wenbo Luo ◽  
Said Jazouli ◽  
Toan Vu-Khanh
Keyword(s):  
Creep Behavior ◽  
Room Temperature ◽  
Multiple Integral ◽  
Model Fit ◽  
Viscoelastic Creep ◽  
Commercial Grade ◽  
Nonlinear Viscoelastic ◽  
Schapery Model ◽  
Special Case ◽  
Better Than

AbstractThe creep behavior of a commercial grade polycarbonate was investigated in this study. 10 different constant stresses ranging from 8 MPa to 50 MPa were applied to the specimen, and the resultant creep strains were measured at room temperature. It was found that the creep could be modeled linearly below 15 MPa, and nonlinearly above 15 MPa. Different nonlinear viscoelastic models have been briefly reviewed and used to fit the test data. It is shown that the Findley model is a special case of the Schapery model, and both the Findley model and the simplified multiple integral representation are suitable for properly describing the creep behavior of the polycarbonate investigated in this paper; however, the Findley model fit the data better than the simplified multiple integral with three terms.

On the dependence structure of hitting times of univariate processes

1988 ◽  
Vol 25 (02) ◽  
pp. 355-362 ◽  
Author(s):  
Nader Ebrahimi ◽  
T. Ramalingam
Keyword(s):  
Brownian Motion ◽  
Structural Properties ◽  
Hitting Times ◽  
Dependence Structure ◽  
Special Case ◽  
New Better Than Used ◽  
Better Than

Some concepts of dependence have recently been introduced by Ebrahimi (1987) to explore the structural properties of the hitting times of bivariate processes. In this framework, the special case of univariate processes has curious features. New properties are derived for this case. Some applications to sequential inference and inequalities for Brownian motion and new better than used (NBU) processes are also provided.

scholarly journals A Performance Study of Some Approximation Algorithms for Computing a Small Dominating Set in a Graph

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 339
Author(s):  
Jonathan Li ◽  
Rohan Potru ◽  
Farhad Shahrokhi
Keyword(s):  
Approximation Algorithms ◽  
Real World ◽  
Hybrid Algorithm ◽  
Dominating Set ◽  
Performance Ratio ◽  
Performance Study ◽  
Similar Time ◽  
Sparse Graphs ◽  
Lp Rounding ◽  
Better Than

We implement and test the performances of several approximation algorithms for computing the minimum dominating set of a graph. These algorithms are the standard greedy algorithm, the recent Linear programming (LP) rounding algorithms and a hybrid algorithm that we design by combining the greedy and LP rounding algorithms. Over the range of test data, all algorithms perform better than anticipated in theory, and have small performance ratios, measured as the size of output divided by the LP objective lower bound. However, each have advantages over the others. For instance, LP rounding algorithm normally outperforms the other algorithms on sparse real-world graphs. On a graph with 400,000+ vertices, LP rounding took less than 15 s of CPU time to generate a solution with performance ratio 1.011, while the greedy and hybrid algorithms generated solutions of performance ratio 1.12 in similar time. For synthetic graphs, the hybrid algorithm normally outperforms the others, whereas for hypercubes and k-Queens graphs, greedy outperforms the rest. Another advantage of the hybrid algorithm is to solve very large problems that are suitable for application of LP rounding (sparse graphs) but LP formulations become formidable in practice and LP solvers crash, as we observed on a real-world graph with 7.7 million+ vertices and a planar graph on 1,000,000 vertices.

ROUTING BALANCED COMMUNICATIONS ON HAMILTON DECOMPOSABLE NETWORKS

2004 ◽  
Vol 14 (03n04) ◽  
pp. 377-385 ◽  
Author(s):  
LADISLAV STACHO ◽  
JOZEF ŠIRÁŇ ◽  
SANMING ZHOU
Keyword(s):  
Wave Length ◽  
Upper Bounds ◽  
Ring Network ◽  
Special Case ◽  
Better Than

In [10] the authors proved upper bounds for the arc-congestion and wave-length number of any permutation demand on a bidirected ring. In this note, we give generalizations of their results in two directions. The first one is that instead of considering only permutation demands we consider any balanced demand, and the second one is that instead of the ring network we consider any Hamilton decomposable network. Thus, we obtain upper bounds (which are best possible in general) for the arc-congestion and wavelength number of any balanced demand on a Hamilton decomposable network. As a special case, we obtain upper bounds on arc- and edge-forwarding indices of Hamilton decomposable networks that are in many cases better than the known ones.

scholarly journals The minimum restricted edge-connected graph and the minimum size of graphs with a given edge–degree

2014 ◽  
Vol 167 ◽  
pp. 304-309
Author(s):  
Weihua Yang ◽  
Yingzhi Tian ◽  
Hengzhe Li ◽  
Hao Li ◽  
Xiaofeng Guo
Keyword(s):  
Connected Graph ◽  
Minimum Size

Bounds on the extinction time distribution of a branching process

1974 ◽  
Vol 6 (2) ◽  
pp. 322-335 ◽  
Author(s):  
Alan Agresti
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Time Distribution ◽  
Branching Process ◽  
Probability Generating Function ◽  
Extinction Time ◽  
Expected Time ◽  
Time To Extinction ◽  
Special Case ◽  
Better Than

The class of fractional linear generating functions, one of the few known classes of probability generating functions whose iterates can be explicitly stated, is examined. The method of bounding a probability generating function g (satisfying g″(1) < ∞) by two fractional linear generating functions is used to derive bounds for the extinction time distribution of the Galton-Watson branching process with offspring probability distribution represented by g. For the special case of the Poisson probability generating function, the best possible bounding fractional linear generating functions are obtained, and the bounds for the expected time to extinction of the corresponding Poisson branching process are better than any previously published.

scholarly journals CKV-type $ B $-matrices and error bounds for linear complementarity problems

2021 ◽  
Vol 6 (10) ◽  
pp. 10846-10860
Author(s):  
Xinnian Song ◽  
◽  
Lei Gao
Keyword(s):  
Error Bound ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Type B ◽  
Numerical Examples ◽  
Infinity Norm ◽  
Norm Bound ◽  
Special Case ◽  
Better Than

<abstract><p>In this paper, we introduce a new subclass of $ P $-matrices called Cvetković-Kostić-Varga type $ B $-matrices (CKV-type $ B $-matrices), which contains DZ-type-$ B $-matrices as a special case, and present an infinity norm bound for the inverse of CKV-type $ B $-matrices. Based on this bound, we also give an error bound for linear complementarity problems of CKV-type $ B $-matrices. It is proved that the new error bound is better than that provided by Li et al. <sup>[<xref ref-type="bibr" rid="b24">24</xref>]</sup> for DZ-type-$ B $-matrices, and than that provided by M. García-Esnaola and J.M. Peña <sup>[<xref ref-type="bibr" rid="b10">10</xref>]</sup> for $ B $-matrices in some cases. Numerical examples demonstrate the effectiveness of the obtained results.</p></abstract>

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