Search results for "Difficult problem"
showing 7 items of 7 documents
Integer Complexity: Experimental and Analytical Results II
2015
We consider representing natural numbers by expressions using only 1’s, addition, multiplication and parentheses. Let \( \left\| n \right\| \) denote the minimum number of 1’s in the expressions representing \(n\). The logarithmic complexity \( \left\| n \right\| _{\log } \) is defined to be \({ \left\| n \right\| }/{\log _3 n}\). The values of \( \left\| n \right\| _{\log } \) are located in the segment \([3, 4.755]\), but almost nothing is known with certainty about the structure of this “spectrum” (are the values dense somewhere in the segment?, etc.). We establish a connection between this problem and another difficult problem: the seemingly “almost random” behaviour of digits in the ba…
OPTIMAL AIRLINE SEAT INVENTORY CONTROL FOR MULTI-LEG FLIGHTS
2005
Abstract For large commercial airlines, efficiently setting and updating seat allocation targets for each passenger category on each multi-leg flight is an extremely difficult problem. This paper presents static and dynamic models of airline seat inventory control for multi-leg flights with multiple fare classes, which allow one to maximize an expected contribution to profit. The dynamic model uses the most recent demand and capacity information and allows one to allocate seats dynamically and anticipatory over time.
Optimal airline seat inventory control for multi‐leg flights
2004
Airline seat inventory control is about “selling the right seats to the right people at the right time”. In this paper, the problem of determining optimal booking policy for multiple fare classes in a pool of identical seats for multi‐leg flights is considered. During the time prior to departure of a multi‐leg flight, decisions must be made concerning the allocation of reserved seats to passengers requesting space on the full or partial spans of the flight. It will be noted that in the case of multi‐leg flights the long‐haul passengers are often unable to obtain seats because the shorter‐haul passengers block them. For large commercial airlines, efficiently setting and updating seat allocat…
Character Tables and Sylow Subgroups Revisited
2018
Suppose that G is a finite group. A classical and difficult problem is to determine how much the character table knows about the local structure of G and vice versa.
A Branch-Price-and-Cut Algorithm for the Min-Max k -Vehicle Windy Rural Postman Problem
2013
[EN] The min-max k -vehicles windy rural postman problem consists of minimizing the maximal distance traveled by a vehicle to find a set of balanced routes that jointly service all the required edges in a windy graph. This is a very difficult problem, for which a branch-and-cut algorithm has already been proposed, providing good results when the number of vehicles is small. In this article, we present a branch-price-and-cut method capable of obtaining optimal solutions for this problem when the number of vehicles is larger for the same set of required edges. Extensive computational results on instances from the literature are presented.
Thermodynamic approach of supercontinuum generation
2009
International audience; This paper is aimed at providing an overview on recent theoretical and experimental works in which a thermodynamic description of the incoherent regime of supercontinuum generation has been formulated. On the basis of the wave turbulence theory, we show that this highly nonlinear and quasi-continuous-wave regime of supercontinuum generation is characterized by two different phenomena. (i) A process of optical wave thermalization ruled by the four-wave mixing effects: The spectral broadening inherent to supercontinuum generation is shown to result from the natural tendency of the optical field to reach its thermodynamic equilibrium state, i. e., the state of maximum n…
Hores: A timetabling system for Spanish secondary schools
1995
Constructing a timetable is a difficult problem faced by every school every year. A feasible solution has to satisfy many different requirements and constraints. A good solution has to provide compact timetables for classes and teachers. In order to help the schools, we have developed HORES, a robust and flexible timetabling system suited to the needs of Spanish secondary schools. HORES runs on a PC and is fast and user-friendly. It may handle virtually every condition required by the schools and obtains good quality solutions in very short computing times. It also allows the user to modify interactively the solutions. HORES is now being used by schools with satisfactory results.