A 3/2-Approximation Algorithm for the Jump Number of Interval Orders
نویسنده
چکیده
The jump number of a partial order P is the minimum number of incomparable adjacent pairs in some linear extension of P. The jump number problem is known to be NP {hard in general. However some particular classes of posets admit easy calculation of the jump number. The complexity status for interval orders still remains unknown. Here we present a heuristic that, given an interval order P , generates a linear extension , whose jump number is less than 3/2 times the jump number of P .
منابع مشابه
The database of interval orders difficult for the jump number minimizing algorithms
The problems of scheduling jobs on a single machine subject to precedence constraints can often be modelled as the jump number problem for posets, where a linear extension of a given partial order is to be found which minimizes the number of noncomparabilities. In this paper, we are investigating a restricted class of posets, called interval orders, admitting approximation algorithms for the ju...
متن کاملComputing the Jump Number on Semi-orders Is Polynomial
1) Introduction and notations In this first section we will give our main definitions and recall different characterizations of interval and semi-orders. In section 2 we shall prove that after a decomposition routine, semi-orders have at most 2 consecutive bumps in a linear extension. We also prove, using a "divide-and-conquer" argument, that computing polynomially the jump number can be done p...
متن کاملClose interval approximation of piecewise quadratic fuzzy numbers for fuzzy fractional program
The fuzzy approach has undergone a profound structural transformation in the past few decades. Numerous studies have been undertaken to explain fuzzy approach for linear and nonlinear programs. While, the findings in earlier studies have been conflicting, recent studies of competitive situations indicate that fractional programming problem has a positive impact on comparative scenario. We pro...
متن کاملUniversal Approximation of Interval-valued Fuzzy Systems Based on Interval-valued Implications
It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy. A formula to compute the lower upper bounds on the number of interval-valued fuzzy sets needed to achieve a pre-specified approximation accuracy for an arbitrary multivariate con...
متن کاملOptimizing the actuation of musculoskeletal model by genetic algorithm to simulate the vertical jump
In human body movement simulation such as vertical jump by a forward dynamic model, optimal control theories must be used. In the recent years, new methods were created for solving optimization problems which they were adopted from animal behaviors and environment events such as Genetic algorithm, Particle swarm and Imperialism competitive. In this work, the skeletal model was constructed by Ne...
متن کامل