THE COMPUTATIONAL COMPLEXITY OF AVOIDING FORBIDDEN SUBMATRICES BY ROW DELETIONS

2006 ◽  
Vol 17 (06) ◽  
pp. 1467-1484 ◽  
Author(s):  
SEBASTIAN WERNICKE ◽  
JOCHEN ALBER ◽  
JENS GRAMM ◽  
JIONG GUO ◽  
ROLF NIEDERMEIER
Keyword(s):  
Close Relation ◽  
Constant Factor ◽  
Input Matrix ◽  
Hitting Set ◽  
Positive Side ◽  
Column Permutation ◽  
Fixed Parameter ◽  
Minimum Number ◽  
Np Complete ◽  
Hitting Set Problem

We initiate a systematic study of the ROW DELETION(B) problem on matrices: Given an input matrix A and a fixed "forbidden submatrix" B, the task is to remove a minimum number of rows from A such that no row or column permutation of B occurs as a submatrix in the resulting matrix. An application of this problem can be found, for instance, in the construction of perfect phylogenies. Establishing a strong connection to variants of the NP-complete HITTING SET problem, we describe and analyze structural properties of B that make ROW DELETION(B)NP-complete. On the positive side, the close relation with HITTING SET problems yields constant-factor polynomial-time approximation algorithms and fixed-parameter tractability results.

Optimal state amalgamation is NP-hard

2017 ◽  
Vol 39 (7) ◽  
pp. 1857-1869 ◽  
Author(s):  
RAFAEL M. FRONGILLO
Keyword(s):  
Finite Type ◽  
Directed Graph ◽  
Symbolic Dynamics ◽  
Hitting Set ◽  
State Splitting ◽  
Continuous Maps ◽  
Np Complete ◽  
Subshifts Of Finite Type ◽  
Hitting Set Problem ◽  
Inverse Operation

A state amalgamation of a directed graph is a node contraction which is only permitted under certain configurations of incident edges. In symbolic dynamics, state amalgamation and its inverse operation, state splitting, play a fundamental role in the theory of subshifts of finite type (SFT): any conjugacy between SFTs, given as vertex shifts, can be expressed as a sequence of symbol splittings followed by a sequence of symbol amalgamations. It is not known whether determining conjugacy between SFTs is decidable. We focus on conjugacy via amalgamations alone and consider the simpler problem of deciding whether one can perform $k$ consecutive amalgamations from a given graph. This problem also arises when using symbolic dynamics to study continuous maps, where one seeks to coarsen a Markov partition in order to simplify it. We show that this state amalgamation problem is NP-complete by reduction from the hitting set problem, thus giving further evidence that classifying SFTs up to conjugacy may be undecidable.

There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration

2014 ◽  
Vol 23 (2) ◽  
pp. 190-217 ◽  
Author(s):  
Gary McGuire ◽  
Bastian Tugemann ◽  
Gilles Civario
Keyword(s):  
Hitting Set ◽  
Minimum Number

APPROXIMATION ALGORITHMS FOR A VARIANT OF DISCRETE PIERCING SET PROBLEM FOR UNIT DISKS

2013 ◽  
Vol 23 (06) ◽  
pp. 461-477 ◽  
Author(s):  
MINATI DE ◽  
GAUTAM K. DAS ◽  
PAZ CARMI ◽  
SUBHAS C. NANDY
Keyword(s):  
Approximation Algorithms ◽  
Simple Algorithm ◽  
Constant Factor ◽  
Performance Ratio ◽  
Approximation Result ◽  
Worst Case ◽  
Approximation Factor ◽  
Minimum Number ◽  
Unit Disks ◽  
Set Of Points

In this paper, we consider constant factor approximation algorithms for a variant of the discrete piercing set problem for unit disks. Here a set of points P is given; the objective is to choose minimum number of points in P to pierce the unit disks centered at all the points in P. We first propose a very simple algorithm that produces 12-approximation result in O(n log n) time. Next, we improve the approximation factor to 4 and then to 3. The worst case running time of these algorithms are O(n8 log n) and O(n15 log n) respectively. Apart from the space required for storing the input, the extra work-space requirement for each of these algorithms is O(1). Finally, we propose a PTAS for the same problem. Given a positive integer k, it can produce a solution with performance ratio [Formula: see text] in nO(k) time.

Input Requirements and Parametric Errors for System Identification Under Periodic Excitation

1972 ◽  
Vol 94 (4) ◽  
pp. 296-302 ◽  
Author(s):  
L. L. Hoberock ◽  
G. W. Stewart
Keyword(s):  
Linear System ◽  
Input State ◽  
Matrix Elements ◽  
Periodic Excitation ◽  
Input Output ◽  
Input Matrix ◽  
Multiple Input ◽  
Minimum Number ◽  
Single Input ◽  
Work Done

This paper provides the conditions on periodic system excitation necessary for unique identification using a multiple input state model of a dynamic system. Results include the minimum number of input frequencies necessary to uniquely determine all state and input matrix elements of an n dimensional linear system. It is shown that this development encompasses earlier work done on single input-output systems. A technique is provided for predicting parametric errors to be expected from identification under periodic excitation, and several examples are used to illustrate these errors.

scholarly journals AN IMPLICIT COVER PROBLEM IN WILD POPULATION STUDY

2010 ◽  
Vol 02 (01) ◽  
pp. 21-31 ◽  
Author(s):  
MARY V. ASHLEY ◽  
TANYA Y. BERGER-WOLF ◽  
WANPRACHA CHAOVALITWONGSE ◽  
BHASKAR DASGUPTA ◽  
ASHFAQ KHOKHAR ◽  
...  
Keyword(s):  
Optimization Problem ◽  
Wild Population ◽  
Combinatorial Optimization Problem ◽  
Set Cover ◽  
Not Given ◽  
Wild Populations ◽  
Feedback Arc Set ◽  
Hitting Set ◽  
Cover Problem ◽  
Hitting Set Problem

In an implicit combinatorial optimization problem, the constraints are not enumerated explicitly but rather stated implicitly through equations, other constraints or auxiliary algorithms. An important subclass of such problems is the implicit set cover (or, equivalently, hitting set) problem in which the sets are not given explicitly but rather defined implicitly. For example, the well-known minimum feedback arc set problem is such a problem. In this paper, we consider such a cover problem that arises in the study of wild populations in biology in which the sets are defined implicitly via the Mendelian constraints and prove approximability results for this problem.

Sign in / Sign up

Export Citation Format

Share Document