60 research outputs found

    Approximability of the Multiple Stack TSP

    Full text link
    STSP seeks a pair of pickup and delivery tours in two distinct networks, where the two tours are related by LIFO contraints. We address here the problem approximability. We notably establish that asymmetric MaxSTSP and MinSTSP12 are APX, and propose a heuristic that yields to a 1/2, 3/4 and 3/2 standard approximation for respectively Max2STSP, Max2STSP12 and Min2STSP12

    Universal Sequencing on a Single Machine

    Get PDF
    We consider scheduling on an unreliable machine that may experience unexpected changes in processing speed or even full breakdowns. We aim for a universal solution that performs well without adaptation for any possible machine behavior. For the objective of minimizing the total weighted completion time, we design a polynomial time deterministic algorithm that finds a universal scheduling sequence with a solution value within 4 times the value of an optimal clairvoyant algorithm that knows the disruptions in advance. A randomized version of this algorithm attains in expectation a ratio of e. We also show that both results are best possible among all universal solutions. As a direct consequence of our results, we answer affirmatively the question of whether a constant approximation algorithm exists for the offline version of the problem when machine unavailability periods are known in advance. When jobs have individual release dates, the situation changes drastically. Even if all weights are equal, there are instances for which any universal solution is a factor of Ω(log n/ log log n) worse than an optimal sequence. Motivated by this hardness, we study the special case when the processing time of each job is proportional to its weight. We present a non-trivial algorithm with a small constant performance guarantee. © 2010 Springer-Verlag

    Drone Base Station Trajectory Management for Optimal Scheduling in LTE-Based Sparse Delay-Sensitive M2M Networks

    Get PDF
    Providing connectivity in areas out of reach of the cellular infrastructure is a very active area of research. This connectivity is particularly needed in case of the deployment of machine type communication devices (MTCDs) for critical purposes such as homeland security. In such applications, MTCDs are deployed in areas that are hard to reach using regular communications infrastructure while the collected data is timely critical. Drone-supported communications constitute a new trend in complementing the reach of the terrestrial communication infrastructure. In this study, drones are used as base stations to provide real-time communication services to gather critical data out of a group of MTCDs that are sparsely deployed in a marine environment. Studying different communication technologies as LTE, WiFi, LPWAN and Free-Space Optical communication (FSOC) incorporated with the drone communications was important in the first phase of this research to identify the best candidate for addressing this need. We have determined the cellular technology, and particularly LTE, to be the most suitable candidate to support such applications. In this case, an LTE base station would be mounted on the drone which will help communicate with the different MTCDs to transmit their data to the network backhaul. We then formulate the problem model mathematically and devise the trajectory planning and scheduling algorithm that decides the drone path and the resulting scheduling. Based on this formulation, we decided to compare between an Ant Colony Optimization (ACO) based technique that optimizes the drone movement among the sparsely-deployed MTCDs and a Genetic Algorithm (GA) based solution that achieves the same purpose. This optimization is based on minimizing the energy cost of the drone movement while ensuring the data transmission deadline missing is minimized. We present the results of several simulation experiments that validate the different performance aspects of the technique

    Dagstuhl Reports : Volume 1, Issue 2, February 2011

    Get PDF
    Online Privacy: Towards Informational Self-Determination on the Internet (Dagstuhl Perspectives Workshop 11061) : Simone Fischer-Hübner, Chris Hoofnagle, Kai Rannenberg, Michael Waidner, Ioannis Krontiris and Michael Marhöfer Self-Repairing Programs (Dagstuhl Seminar 11062) : Mauro Pezzé, Martin C. Rinard, Westley Weimer and Andreas Zeller Theory and Applications of Graph Searching Problems (Dagstuhl Seminar 11071) : Fedor V. Fomin, Pierre Fraigniaud, Stephan Kreutzer and Dimitrios M. Thilikos Combinatorial and Algorithmic Aspects of Sequence Processing (Dagstuhl Seminar 11081) : Maxime Crochemore, Lila Kari, Mehryar Mohri and Dirk Nowotka Packing and Scheduling Algorithms for Information and Communication Services (Dagstuhl Seminar 11091) Klaus Jansen, Claire Mathieu, Hadas Shachnai and Neal E. Youn

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

    Get PDF
    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    Comparing a New Algorithm for the Traveling Salesman Problem to Previous Deterministic and Stochastic Algorithms

    Full text link
    The challenges of drone navigation have driven many advances in the development of autonomous systems. Unmanned Autonomous Vehicles(UAVs) operate in a rapidly changing flight space and have to balance a complex set of constraints and objectives. Many of these objectives can be represented in variations of the classic Traveling Salesman Problem. Numerous approximate solutions to TSP have been proposed over the years, but these approaches have difficulty when adding new constraints that require rapid recalculation of the solution. Either they are fast but do not provide solutions that are close to the optimum, or they provide excellent solutions but they take a large number of computational resources to arrive at a solution. We are proposing a new algorithm that will be able to provide a very competitive solution to TSP compared to other probabilistic and deterministic approaches. We will demonstrate that this new algorithm is robust and efficient enough to be effective within the strict computational constraints of a typical UAV avionics system

    The Catalog Problem:Deep Learning Methods for Transforming Sets into Sequences of Clusters

    Get PDF
    The titular Catalog Problem refers to predicting a varying number of ordered clusters from sets of any cardinality. This task arises in many diverse areas, ranging from medical triage, through multi-channel signal analysis for petroleum exploration to product catalog structure prediction. This thesis focuses on the latter, which exemplifies a number of challenges inherent to ordered clustering. These include learning variable cluster constraints, exhibiting relational reasoning and managing combinatorial complexity. All of which present unique challenges for neural networks, combining elements of set representation, neural clustering and permutation learning.In order to approach the Catalog Problem, a curated dataset of over ten thousand real-world product catalogs consisting of more than one million product offers is provided. Additionally, a library for generating simpler, synthetic catalog structures is presented. These and other datasets form the foundation of the included work, allowing for a quantitative comparison of the proposed methods’ ability to address the underlying challenge. In particular, synthetic datasets enable the assessment of the models’ capacity to learn higher order compositional and structural rules.Two novel neural methods are proposed to tackle the Catalog Problem, a set encoding module designed to enhance the network’s ability to condition the prediction on the entirety of the input set, and a larger architecture for inferring an input- dependent number of diverse, ordered partitional clusters with an added cardinality prediction module. Both result in an improved performance on the presented datasets, with the latter being the only neural method fulfilling all requirements inherent to addressing the Catalog Problem

    Algorithmes d'approximation pour des programmes linéaires et les problèmes de Packing avec des contraintes géometriques

    Get PDF
    In this thesis we approach several problems with approximation algorithms; these are feasibility problems as well as optimization problems. In Chapter 1 we give a brief introduction into the general paradigm of approximation algorithms, motivate the problems, and give an outline of the thesis. In Chapter 2, we discuss two algorithms to approximately generate a feasible solution of the mixed packing and covering problem which is a model from convex optimization. This problem includes a large class of linear programs. The algorithms generate approximately feasible solutions within O(M(ln M+epsilon^{-2} ln epsilon^{-1})) and O(M epsilon{-2} ln (M epsilon^{-1}))iterations,respectively,whereineachiterationablockproblemwhichdependsonthespecificapplicationhastobesolved.Bothalgorithms,appliedtolinearprograms,canresultincolumngenerationalgorithms.InChapter3,weimplementanalgorithmfortheso−calledmax−min−resourcesharingproblem.Thisisacertainconvexoptimizationproblemwhich,similartotheprobleminChapter1,includesalargeclassoflinearprograms.Theimplementation,whichisincludedintheappendix,isdoneinC++.WeusetheimplementationinthecontextofanAFPTASforStripPackinginordertoevaluatedynamicoptimizationofaparameterinthealgorithm,namelythesteplengthusedforinterpolation.Wecompareourchoicetothestaticsteplengthproposedintheanalysisofthealgorithmandconcludethatdynamicoptimizationofthesteplengthsignificantlyreducesthenumberofiterations.InChapter4,westudytwocloselyrelatedschedulingproblems,namelynon−preemptiveschedulingwithfixedjobsandschedulingwithnon−availabilityforsequentialjobsonmidenticalmachinesunderthemakespanobjective,wheremisconstant.Forthefirstproblem,whichdoesnotadmitanFPTASunlessP=NP,weobtainanewPTAS.Forthesecondproblem,weshowthatasuitablerestriction(namelythepermanentavailabilityofonemachine)isnecessarytoobtainaboundedapproximationratio.Forthisrestriction,whichdoesnotadmitanFPTASunlessP=NP,wepresentaPTAS;wealsodiscussthecomplexityofvariousspecialcases.Intotal,theresultsarebasicallybestpossible.InChapter5,wecontinuethestudiesfromChapter4wherenowthenumbermofmachinesispartoftheinput,whichmakestheproblemalgorithmicallyharder.Schedulingwithfixedjobsdoesnotadmitanapproximationratiobetterthan3/2,unlessP=NP;hereweobtainanapproximationratioof3/2+epsilonforanyepsilon>0.Forschedulingwithnon−availability,werequireaconstantpercentageofthemachinestobepermanentlyavailable.Thisrestrictionalsodoesnotadmitanapproximationratiobetterthan3/2unlessP=NP;wealsoobtainanapproximationratioof iterations, respectively, where in each iteration a block problem which depends on the specific application has to be solved. Both algorithms, applied to linear programs, can result in column generation algorithms. In Chapter 3, we implement an algorithm for the so-called max-min-resource sharing problem. This is a certain convex optimization problem which, similar to the problem in Chapter 1, includes a large class of linear programs. The implementation, which is included in the appendix, is done in C++. We use the implementation in the context of an AFPTAS for Strip Packing in order to evaluate dynamic optimization of a parameter in the algorithm, namely the step length used for interpolation. We compare our choice to the static step length proposed in the analysis of the algorithm and conclude that dynamic optimization of the step length significantly reduces the number of iterations. In Chapter 4, we study two closely related scheduling problems, namely non-preemptive scheduling with fixed jobs and scheduling with non-availability for sequential jobs on m identical machines under the makespan objective, where m is constant. For the first problem, which does not admit an FPTAS unless P=NP, we obtain a new PTAS. For the second problem, we show that a suitable restriction (namely the permanent availability of one machine) is necessary to obtain a bounded approximation ratio. For this restriction, which does not admit an FPTAS unless P=NP, we present a PTAS; we also discuss the complexity of various special cases. In total, the results are basically best possible. In Chapter 5, we continue the studies from Chapter 4 where now the number m of machines is part of the input, which makes the problem algorithmically harder. Scheduling with fixed jobs does not admit an approximation ratio better than 3/2, unless P=NP; here we obtain an approximation ratio of 3/2+epsilon for any epsilon>0. For scheduling with non-availability, we require a constant percentage of the machines to be permanently available. This restriction also does not admit an approximation ratio better than 3/2 unless P=NP; we also obtain an approximation ratio of 3/2+\epsilon$ for any epsilon>0. With an interesting argument, the approximation ratio for both problems is refined to exactly 3/2. We also point out an interesting relation of scheduling with fixed jobs to Bin Packing. As in Chapter 4, the results are in a certain sense best possible. Finally, in Chapter 6, we conclude with some remarks and open research problems
    • …
    corecore