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On the Approximability of the Minimum Test Collection Problem [chapter]

Bjarni V. Halldórsson, Magnús M. Halldórsson, R. Ravi
2001 Lecture Notes in Computer Science  
The minimum test collection problem is defined as follows.  ...  Given a ground set S and a collection C of tests (subsets of S), find the minimum subcollection C of C such that for every pair of elements (x, y) in S there exists a test in C that contains exactly one  ...  Their result, combined with the hardness of approximation results on set covering [2, 4, 15] already imply a logarithmic lower bound on the approximation ratio of minimum test collection (Theorems 2  ... 
doi:10.1007/3-540-44676-1_13 fatcat:mnaoakykizbbxlzobwxeymwjgi

Alarm placement in systems with fault propagation

K.B. Lakshmanan, Daniel J. Rosenkrantz, S.S. Ravi
2000 Theoretical Computer Science  
Finally, we demonstrate the connection between the minimum alarm set problem and the minimum test collection problem, and prove similar results. : S 0 3 0 4 -3 9 7 5 ( 9 8 ) 0 0 2 1 4 -X  ...  We then present a polynomial-time approximation algorithm for the general case which guarantees that the ratio of the number of alarms placed to the optimum required is within a factor that is logarithmic  ...  In particular, [17] was brought to their attention by one of the referees.  ... 
doi:10.1016/s0304-3975(98)90214-6 fatcat:p44dfbpm6bhljfg2nfxxeogtgq

Using Viruses to Improve GAs [chapter]

Francesco Pappalardo
2005 Lecture Notes in Computer Science  
In this paper, we will introduce an evolutionary algorithm for finding approximate solutions to the Weighted Minimum Hitting Set Problem.  ...  We will test its performance against a well known and efficient greedy algorithm, and on several families of sets.  ...  Hence, we were able to test its performance even on different problems such as the Minimum Vertex Cover Problem.  ... 
doi:10.1007/11539902_19 fatcat:ghib2hm7fbfh3dl72rkgek5pnq

Page 92 of The Southern Journal of Educational Research Vol. 2, Issue 2 [page]

1968 The Southern Journal of Educational Research  
The three tests were given one week apart. The non-numer- ical problem test was administered first. One week later, the first part of the numerical problem test was administered.  ...  Collecting the Data Data Collected from Subjects Basically, the data that were collected directly from the students used in the study consisted of the scores on the three tests in the instrument and such  ... 

Page 858 of Mathematical Reviews Vol. , Issue 83b [page]

1983 Mathematical Reviews  
This involves breaking the problem down into a master problem and one or more subproblems, which are all solved iteratively, exchanging information between the subproblems on one hand and the master on  ...  “We have produced a relatively large collection of carefully coded test functions and designed very simple procedures for testing the reliability and robustness of unconstrained optimization software.  ... 

Page 5366 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
We confirm that the minimum domination number of the 8 x 8 grid graph is 16, the minimum domination number of the 8 x 9 grid graph is greater than 17, and the minimum domination number of the 9 x 9 grid  ...  When each vertex of the input graph is partitioned into a separate subcell, a set of vertices is collected from those subcells which have the content equal to one.  ... 

Page 1277 of Mathematical Reviews Vol. , Issue 99b [page]

1991 Mathematical Reviews  
The approximation factors are improved from 2 to : for both of the problems, yet the techniques 99b:68148 involved are all based on augmenting depth-first-search trees and no similar progress has been  ...  1277 68R Discrete mathematics in relation to computer science the adaptive sampling (AS) algorithm which solves the problem of estimating the number M of distinct elements of a large collection of n data  ... 

Steiner Tree Problems With Profits

Alysson Costa, Jean-François Cordeau, Gilbert Laporte
2006 INFOR. Information systems and operational research  
The problem of determining a minimum cost network spanning all vertices V of G is known as the Minimum Spanning Tree Problem (MSTP).  ...  Therefore, four basic criteria can be used to distinguish between the variants: the cost of edges, the revenue of vertices, the minimum collected revenue (quota), and the maximum allowed cost (budget).  ...  Acknowledgments This work was supported by the Brazilian Federal Agency for Post-Graduate Education -CAPES, under grant BEX 1097/01-6 and by the Canadian Natural Science and Engineering Research Council  ... 
doi:10.1080/03155986.2006.11732743 fatcat:uxm7hy6nujhsdhlsdb5kwl6u6a

Non-unique probe selection and group testing

Feng Wang, Hongwei David Du, Xiaohua Jia, Ping Deng, Weili Wu, David MacCallum
2007 Theoretical Computer Science  
Then any feasible solution of Min-d-DS contains at least s+ (n-s)(d+1)/2 pools. • The minimum 1-separable submatrix problem is also called the minimum test set (the minimum test cover, the minimum test  ...  Given n items with some positive ones, identify all positive ones by less number of tests. • Each test is on a subset of items. • Test outcome is positive iff there is a positive item in the subset.  ...  • The feasible solution obtained in the above algorithm is a polynomial-time approximation with performance ratio 1+2/(d+1).  ... 
doi:10.1016/j.tcs.2007.02.067 fatcat:fy4pplicmzajrdx5k2o6zklyeq

Page 7080 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
(1-WI-C; Madison, WI) On testing for zero polynomials by a set of points with bounded precision.  ...  The authors present the first constant-factor approximation algo- rithm for a fundamental problem: the store-and-forward packet routing problem on arbitrary networks.  ... 

Page 4322 of Mathematical Reviews Vol. , Issue 2000f [page]

2000 Mathematical Reviews  
For the test problems from the Harwell-Boeing collection and some other applications, the performance of our preconditioners can be comparable or superior to incomplete LU preconditioners with similar  ...  We show that a family of uniform preconditioners for the corresponding problem on the extended, or fictitious, domain leads directly to uniform preconditioners for the original problem.  ... 

Page 2586 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
Joseph (IL-TECH-C; Haifa) Approximation algorithms for network design problems on bounded subsets.  ...  Summary: “The problem of finding minimum-weight spanning subgraphs with a given connectivity requirement is considered. The problem is NP-hard when the connectivity requirement is greater than one.  ... 

Tight approximability results for test set problems in bioinformatics

Piotr Berman, Bhaskar DasGupta, Ming-Yang Kao
2005 Journal of computer and system sciences (Print)  
For most versions of the problem, including the latter, we establish matching lower and upper bounds on approximation ratio.  ...  In the simplest version, a test is a subset of the universe and two objects are distinguished by our collection if one test contains exactly one of them.  ...  We would like to thank the following persons: (a) Venkatram Vishwanath for implementing and evaluating various algorithms, (b) Dan Gusfield and Sam Rash for providing their experimental data and discussions  ... 
doi:10.1016/j.jcss.2005.02.001 fatcat:bosflbsoafgphpgg72pybidxq4

Tight Approximability Results for Test Set Problems in Bioinformatics [chapter]

Piotr Berman, Bhaskar DasGupta, Ming-Yang Kao
2004 Lecture Notes in Computer Science  
For most versions of the problem, including the latter, we establish matching lower and upper bounds on approximation ratio.  ...  In the simplest version, a test is a subset of the universe and two objects are distinguished by our collection if one test contains exactly one of them.  ...  We would like to thank the following persons: (a) Venkatram Vishwanath for implementing and evaluating various algorithms, (b) Dan Gusfield and Sam Rash for providing their experimental data and discussions  ... 
doi:10.1007/978-3-540-27810-8_5 fatcat:bgj7svkbojapdnar7ytbhfewnm

Page 7281 of Mathematical Reviews Vol. , Issue 98K [page]

1998 Mathematical Reviews  
On the other hand, we give efficient algorithms for the related problems of randomized equality testing and testing for a given occurrence of an un- compressed pattern.  ...  ., 1180, Springer, Berlin, 1996 Summary: “We consider the problems of computing r-approximate traveling salesman tours and r-approximate minimum spanning trees for a set of m points in R“, where d > |  ... 
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