arXiv subjects

Jinchuan Cui

Publications and source records attributed to Jinchuan Cui.

5 recordsLinked to original sources

arXiv2023

The airplane refueling problem is NP-complete and is solvable in polynomial time

The airplane refueling problem is a nonlinear combinatorial optimization problem, and its equivalent problem the $n$-vehicle exploration problem is proved to be NP-complete (arXiv:2304.03965v1, The $n$-vehicle exploration problem is NP-complete). In Article (arXiv:2210.11634v2, A polynomial-time algorithm to solve the aircraft refueling problem: the sequential search algorithm), we designed the sequential search algorithm for solving large scale of airplane refueling instances, and we proved that the computational complexity increases to polynomial time with increasing number of airplanes. Thus the airplane refueling problem, as an NP-complete problem, is solvable in polynomial time when its input scale is sufficiently large.

cs.CC↗

arXiv2023

The n-vehicle exploration problem is NP-complete

The $n$-vehicle exploration problem (NVEP) is a nonlinear unconstrained optimization problem. Given a fleet of $n$ vehicles with mid-trip refueling technique, the NVEP tries to find a sequence of $n$ vehicles to make one of the vehicles travel the farthest, and at last all the vehicles return to the start point. NVEP has a fractional form of objective function, and its computational complexity of general case remains open. Given a directed graph $G$, it can be reduced in polynomial time to an instance of NVEP. We prove that the graph $G$ has a hamiltonian path if and only if the reduced NVEP instance has a feasible sequence of length at least $n$. Therefore we show that Hamiltonian path $\leq_P$ NVEP, and consequently prove that NVEP is NP-complete.

cs.CC↗

arXiv2022

A Polynomial-time Algorithm to Solve the Airplane Refueling Problem: the Sequential Search Algorithm

Airplane refueling problem is a nonlinear unconstrained optimization problem with $n!$ feasible solutions. Given a fleet of $n$ airplanes with mid-air refueling technique, the question is to find the best refueling policy to make the last remaining airplane travel the farthest. In order to solve airplane refueling problem, we proposed the definition of sequential feasible solution by employing the refueling properties of data structure. We proved that if an airplane refueling instance has feasible solutions, it must have sequential feasible solutions; and the optimal feasible solution must be the optimal sequential feasible solution. So we need to numerate all the sequential feasible solutions to get an exact algorithm. We proposed the sequential search algorithm which consists of two steps, the first step of which aims to seek out all of the sequential feasible solutions, and the second step aims to search for the maximal sequential feasible solution by bubble sorting all of the sequential feasible solutions. We observed that the number of the sequential feasible solutions will change to grow at a polynomial rate when the input size of $n$ is greater than an inflection point $N$. Then we proved that the sequential search algorithm is a polynomial-time algorithm to solve the airplane refueling problem. Moreover, we built an efficient computability scheme, according to which we could forecast within a polynomial time the computational complexity of the sequential search algorithm that runs on any given airplane refueling instance. Thus we could provide a computational strategy for decision makers or algorithm users by considering with their available computing resources.

cs.DS↗

arXiv2019

A Fast Exact Algorithm for Airplane Refueling Problem

We consider the airplane refueling problem, where we have a fleet of airplanes that can refuel each other. Each airplane is characterized by specific fuel tank volume and fuel consumption rate, and the goal is to find a drop out order of airplanes that last airplane in the air can reach as far as possible. This problem is equivalent to the scheduling problem $1||\sum w_j (- \frac{1}{C_j})$. Based on the dominance properties among jobs, we reveal some structural properties of the problem and propose a recursive algorithm to solve the problem exactly. The running time of our algorithm is directly related to the number of schedules that do not violate the dominance properties. An experimental study shows our algorithm outperforms state of the art exact algorithms and is efficient on larger instances.

cs.DS↗

arXiv2011

A variant of multitask n-vehicle exploration problem: maximizing every processor's average profit

We discuss a variant of multitask n-vehicle exploration problem. Instead of requiring an optimal permutation of vehicles in every group, the new problem asks all vehicles in a group to arrive at a same destination. It can also be viewed as to maximize every processor's average profit, given n tasks, and each task's consume-time and profit. Meanwhile, we propose a new kind of partition problem in fractional form, and analyze its computational complexity. Moreover, by regarding fractional partition as a special case, we prove that the maximizing average profit problem is NP-hard when the number of processors is fixed and it is strongly NP-hard in general. At last, a pseudo-polynomial time algorithm for the maximizing average profit problem and the fractional partition problem is presented, thanks to the idea of the pseudo-polynomial time algorithm for the classical partition problem.

math.OC↗