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COMPUTER SCIENCE (1187 journals)            First | 5 6 7 8 9 10 11 12     

Journal of Interaction Science     Open Access  
Journal of Interactive Humanities     Open Access   (Followers: 1)
Journal of Interactive Marketing     Hybrid Journal   (Followers: 4)
Journal of Interactive Media in Education     Open Access   (Followers: 5)
Journal of K-Theory     Full-text available via subscription   (Followers: 1)
Journal of Kufa for Mathematics and Computer     Open Access  
Journal of Laboratory Automation     Hybrid Journal  
Journal of Language Modelling     Open Access  
Journal of Law, Information and Science     Full-text available via subscription   (Followers: 24)
Journal of Location Based Services     Hybrid Journal   (Followers: 2)
Journal of Logic and Computation     Hybrid Journal  
Journal of Manufacturing Systems     Full-text available via subscription   (Followers: 6)
Journal of Material Cycles and Waste Management     Hybrid Journal   (Followers: 2)
Journal of mathematical and computational science     Open Access   (Followers: 5)
Journal of Mathematical Imaging and Vision     Hybrid Journal   (Followers: 2)
Journal of Medical Systems     Hybrid Journal   (Followers: 2)
Journal of Metallurgy     Open Access   (Followers: 2)
Journal of Mobile, Embedded and Distributed Systems     Open Access   (Followers: 2)
Journal of Molecular Structure     Hybrid Journal   (Followers: 3)
Journal of Multimedia     Open Access   (Followers: 2)
Journal of Multivariate Analysis     Hybrid Journal   (Followers: 4)
Journal of Nanoparticle Research     Hybrid Journal   (Followers: 3)
Journal of Network and Computer Applications     Hybrid Journal   (Followers: 3)
Journal of Network and Systems Management     Hybrid Journal  
Journal of Networks     Open Access   (Followers: 4)
Journal of Neural Transmission     Hybrid Journal   (Followers: 2)
Journal of Number Theory     Full-text available via subscription   (Followers: 1)
Journal of Optical and Fiber Communications Reports     Hybrid Journal   (Followers: 2)
Journal of Optimization Theory and Applications     Hybrid Journal   (Followers: 2)
Journal of Organizational and End User Computing     Full-text available via subscription   (Followers: 2)
Journal of Organizational Behavior     Hybrid Journal   (Followers: 26)
Journal of Organizational Computing and Electronic Commerce     Hybrid Journal   (Followers: 2)
Journal of Parallel and Distributed Computing     Hybrid Journal   (Followers: 6)
Journal of Policy Analysis and Management     Hybrid Journal   (Followers: 14)
Journal of Process Control     Hybrid Journal   (Followers: 2)
Journal of Proteome Science and Computational Biology     Open Access  
Journal of Real-Time Image Processing     Hybrid Journal   (Followers: 7)
Journal of Revenue and Pricing Management     Partially Free   (Followers: 5)
Journal of Scheduling     Hybrid Journal   (Followers: 3)
Journal of Science and Technology of the Arts     Open Access   (Followers: 2)
Journal of Scientific Computing     Hybrid Journal   (Followers: 2)
Journal of Second Language Writing     Hybrid Journal   (Followers: 14)
Journal of Sensor Technology     Open Access   (Followers: 2)
Journal of Sensors     Open Access   (Followers: 7)
Journal of Signal Processing Systems     Hybrid Journal  
Journal of Software     Open Access   (Followers: 1)
Journal of Software : Evolution and Process     Hybrid Journal   (Followers: 2)
Journal of Software Engineering     Open Access   (Followers: 6)
Journal of Solar Energy Engineering     Full-text available via subscription   (Followers: 17)
Journal of Spatial Information Science     Open Access   (Followers: 1)
Journal of Statistical Software     Open Access   (Followers: 8)
Journal of Symbolic Computation     Hybrid Journal   (Followers: 1)
Journal of Systems and Software     Hybrid Journal   (Followers: 6)
Journal of Systems Architecture     Hybrid Journal   (Followers: 3)
Journal of Systems Integration     Open Access   (Followers: 1)
Journal of Systems Science and Complexity     Hybrid Journal   (Followers: 5)
Journal of Systems Science and Systems Engineering     Hybrid Journal   (Followers: 2)
Journal of Telecommunications Management     Full-text available via subscription   (Followers: 2)
Journal of the ACM     Full-text available via subscription   (Followers: 1)
Journal of the American Medical Informatics Association     Full-text available via subscription   (Followers: 14)
Journal of the Association for History and Computing     Open Access   (Followers: 4)
Journal of the Brazilian Computer Society     Open Access  
Journal of the Text Encoding Initiative     Open Access   (Followers: 1)
Journal of Theoretical and Computational Chemistry     Hybrid Journal   (Followers: 7)
Journal of Transplantation     Open Access   (Followers: 3)
Journal of Transportation Systems Engineering and Information Technology     Full-text available via subscription   (Followers: 13)
Journal of Turbulence     Hybrid Journal  
Journal of Urban Regeneration and Renewal     Full-text available via subscription   (Followers: 9)
Journal of Visual Communication and Image Representation     Hybrid Journal   (Followers: 5)
Journal of VLSI Design Tools & Technology     Full-text available via subscription  
Journal of Water and Land Development     Open Access   (Followers: 1)
Journal of Zhejiang University SCIENCE C     Hybrid Journal  
Journal on Chain and Network Science     Full-text available via subscription   (Followers: 2)
Journal on Data Semantics     Hybrid Journal   (Followers: 2)
Journal on Multimodal User Interfaces     Hybrid Journal   (Followers: 3)
Jurnal Ilmu Komputer dan Informasi     Open Access  
Jurnal Informatika     Open Access   (Followers: 2)
Jurnal Informatika     Open Access   (Followers: 3)
Jurnal INKOM : Jurnal Informatika, Sistem Kendali dan Komputer     Open Access   (Followers: 1)
Jurnal Sistem Komputer     Open Access  
Jurnal Teknologi     Open Access   (Followers: 1)
KI - K√ľnstliche Intelligenz     Hybrid Journal  
Knowledge and Information Systems     Hybrid Journal   (Followers: 10)
Knowledge Management Research & Practice     Hybrid Journal   (Followers: 14)
Kybernetes     Hybrid Journal   (Followers: 1)
Landscape and Ecological Engineering     Hybrid Journal   (Followers: 3)
Language & Communication     Hybrid Journal   (Followers: 14)
Language Resources and Evaluation     Hybrid Journal   (Followers: 6)
Learning Technologies, IEEE Transactions on     Hybrid Journal   (Followers: 10)
Lecture Notes in Computer Science     Hybrid Journal   (Followers: 1)
Legal Theory     Hybrid Journal   (Followers: 7)
Leonardo     Hybrid Journal   (Followers: 9)
Library Hi Tech News     Hybrid Journal   (Followers: 704)
Library Technology Reports     Full-text available via subscription   (Followers: 174)
Linear Algebra and its Applications     Full-text available via subscription   (Followers: 5)
Literary and Linguistic Computing     Hybrid Journal   (Followers: 6)
LMS Journal of Computation and Mathematics     Free  
Logic and Analysis     Hybrid Journal  
Logica Universalis     Hybrid Journal  
Macromolecular Reaction Engineering     Hybrid Journal  

  First | 5 6 7 8 9 10 11 12     

Journal Cover Journal of Scheduling
   [5 followers]  Follow    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
     ISSN (Print) 1099-1425 - ISSN (Online) 1094-6136
     Published by Springer-Verlag Homepage  [2210 journals]   [SJR: 1.857]   [H-I: 34]
  • Integer programming for the generalized high school timetabling problem
    • Abstract: Abstract Recently, the XHSTT format for high school timetabling was introduced. It provides a uniform way of modeling problem instances and corresponding solutions. The format supports a wide variety of constraints, and currently 38 real-life instances from 11 different countries are available. Thereby, the XHSTT format serves as a common ground for researchers within this area. This paper describes the first exact method capable of handling an arbitrary instance of the XHSTT format. The method is based on a mixed-integer linear programming (MIP) model, which is solved in two steps with a commercial general-purpose MIP solver. Computational results show that our approach is able to find previously unknown optimal solutions for 2 instances of XHSTT and proves optimality of 4 known solutions. For the instances not solved to optimality, new non-trivial lower bounds were found in 11 cases, and new best known solutions were found in 9 cases. Furthermore, the approach is compared with the finalists of Round 2 of the International Timetabling Competition 2011 and is shown to be competitive with one of the finalists.
      PubDate: 2014-12-09
  • Improved upper bounds for online malleable job scheduling
    • Abstract: Abstract In this paper, we study online algorithms that schedule malleable jobs, i.e., jobs that can be parallelized on any subset of the available \(m\) identical machines. We study a model that accounts for the tradeoff between multiprocessor speedup and overhead time, namely, if job \(j\) has processing requirement \(p_j\) and is assigned to run on \(k_j\) machines, then \(j\) ’s execution time becomes \(p_j/k_j + (k_j -1)c\) , where \(c\) is a constant parameter to the problem. For \(m=2\) , we present an online algorithm OCS that has a strong competitive ratio of 3/2, matching a previously established lower bound. We also present an online algorithm ASYM2 that is asymptotically \(((4-\epsilon )/(3-\epsilon ))\) -competitive when \(m=2\) , where \(0 < \epsilon \le 2\) is a parameter to the algorithm, improving upon an existing asymptotically (3/2)-competitive algorithm. Finally, we present an online algorithm OTO that is strongly \(2\) -competitive when \(m = 3\) , improving upon the previous best upper bound of \(9/4\) .
      PubDate: 2014-12-09
  • Energetic reasoning for energy-constrained scheduling with a continuous
    • Abstract: Abstract This paper addresses a scheduling problem with continuous resources and energy constraints. Given a set of non-preemptive activities, each activity requires a continuously divisible resource whose instantaneous usage is limited in maximum and minimum, its processing satisfying a time window and a total energy (time \(\times \) resource-usage) requirement. The goal consists of getting a schedule satisfying all the constraints. The problem, which we refer to as the Energy-Constrained Scheduling Problem with Continuous Resources (CECSP), is a generalization of the well-known cumulative scheduling problem for which the “energetic reasoning” or “left-shift/right-shift” necessary feasibility condition yielded a popular polynomially computable satisfiability test. The paper presents a generalization of the energetic reasoning for the CECSP, defining precisely the activity minimum consumptions and exhibiting a polynomial number of relevant time intervals on which it is sufficient to apply the satisfiability tests. A strongly polynomial energetic reasoning satisfiability test can be derived for the considered generalization, which also yields a short proof for the complexity of the original algorithm. Some limits of the approach, as well as an approximation framework for more general resource consumption functions, are also addressed.
      PubDate: 2014-12-03
  • Generating class schedules within a complex modular environment with
           application to secondary schools
    • Abstract: Abstract Westside High School (WHS) of Omaha, Nebraska utilizes a sophisticated scheduling environment called “modular scheduling.” Modular scheduling empowers teachers with the ability to design the structure of their classes by adjusting the frequency, duration, and location of each of their lessons. This paper presents a novel heuristic methodology, implemented as a computer program called the sequential modular algorithmic routines for timetabling (SMART) Scheduler, which creates cohesive modular class schedules using effective techniques such as ejection trees and student sectioning. In experimentation, the SMART Scheduler is able to schedule over 2,800 distinct lessons in less than 4 s using data provided by WHS. This paper describes algorithms within the SMART Scheduler as well as computational results of its implementation.
      PubDate: 2014-12-02
  • A mixed-integer linear programming approach to the optimization of
           event-bus schedules: a scheduling application in the tourism sector
    • Abstract: Abstract This paper deals with “The Enchanted Journey,” which is a daily event tour booked by Bollywood-film fans. During the tour, the participants visit original sites of famous Bollywood films at various locations in Switzerland; moreover, the tour includes stops for lunch and shopping. Each day, up to five buses operate the tour. For operational reasons, however, two or more buses cannot stay at the same location simultaneously. Further operative constraints include time windows for all activities and precedence constraints between some activities. The planning problem is how to compute a feasible schedule for each bus. We implement a two-step hierarchical approach. In the first step, we minimize the total waiting time; in the second step, we minimize the total travel time of all buses. We present a basic formulation of this problem as a mixed-integer linear program. We enhance this basic formulation by symmetry-breaking constraints, which reduces the search space without loss of generality. We report on computational results obtained with the Gurobi Solver. Our numerical results show that all relevant problem instances can be solved using the basic formulation within reasonable CPU time, and that the symmetry-breaking constraints reduce that CPU time considerably.
      PubDate: 2014-12-01
  • Processing time generation schemes for parallel machine scheduling
           problems with various correlation structures
    • Abstract: Abstract This research considers the generation of random processing times for parallel machine scheduling problems. We present several processing time generation schemes that consider different levels and combinations of machine correlation and job correlation. Also, metrics to evaluate the amounts of machine relatedness and job uniformity for the randomly generated processing times of a given problem instance are presented. The proposed schemes generate desirable problem instances that can be used to test different solution approaches (such as heuristics, dynamic programming, and branch-and-bound). Computational results indicate that the schemes provide problem instances with many desirable properties.
      PubDate: 2014-12-01
  • Review of real-time vehicle schedule recovery methods in transportation
    • Abstract: Abstract This paper presents a comprehensive review on methods for real-time schedule recovery in transportation services. The survey concentrates on published research on recovery of planned schedules in the occurrence of one or several severe disruptions such as vehicle breakdowns, accidents, and delays. Only vehicle assignment and rescheduling are reviewed; crew scheduling and passenger logistics problems during disruptions are not. Real-time vehicle schedule recovery problems (RTVSRP) are classified into three classes: vehicle rescheduling, for road-based services, train-based rescheduling, and airline schedule recovery problems. For each class, a classification of the models is presented based on problem formulations and solution strategies. The paper concludes that RTVSRP is a challenging problem that requires quick and good quality solutions to very difficult and complex situations, involving several different contexts, restrictions, and objectives. The paper also identifies research gaps to be investigated in the future, stimulating research in this area.
      PubDate: 2014-12-01
  • An analysis of constructive algorithms for the airport baggage sorting
           station assignment problem
    • Abstract: Abstract The assignment of airport resources can significantly affect the quality of service provided by airlines and airports. High quality assignments can support airlines and airports in adhering to published schedules by minimising changes or delays while waiting for resources to become available. In this paper, we consider the problem of assigning available baggage sorting stations to flights which have already been scheduled and allocated to stands. A model for the problem is presented, and the different objectives which have to be considered are highlighted. A number of constructive algorithms for sorting station assignments are then presented and their effects are compared and analysed when different numbers of sorting stations are available. It can be observed that appropriate algorithm selection is highly dependent upon whether or not reductions in service time are permitted and upon the flight density in relation to the number of sorting stations. Finally, since these constructive approaches produce different solutions which are better for different trade-offs of the objectives, we utilise these as initial solutions for an evolutionary algorithm as well as for an Integer Linear Programming model in CPLEX. We show that in both cases they are helpful for improving the results which are obtainable within reasonable solution times.
      PubDate: 2014-12-01
  • A reduction approach to the two-campus transport problem
    • Abstract: Abstract The two-campus transport problem (TCTP) is a dial-a-ride problem with only two destinations. The problem is motivated by a transport problem between two campuses of an academic college. The two campuses are located in two different cities. Lecturers living in one city are sometimes asked to teach at the other city’s campus. The problem is that of transporting the lecturers from one campus to the other, using a known set of vehicles, so as to minimize the time the lecturers wait for their transport. We mathematically model the general TCTP, and provide an algorithm that solves it, which is polynomial in the number of lecturers. The algorithm is based on a reduction to a shortest path problem.
      PubDate: 2014-12-01
  • Scheduling of parallel machines with sequence-dependent batches and
           product incompatibilities in an automotive glass facility
    • Abstract: Abstract This application is motivated by a complex real-world scheduling problem found in the bottleneck workstation of the production line of an automotive safety glass manufacturing facility. The scheduling problem consists of scheduling jobs (glass parts) on a number of parallel batch processing machines (furnaces), assigning each job to a batch, and sequencing the batches on each machine. The two main objectives are to maximize the utilization of the parallel machines and to minimize the delay in the completion date of each job in relation to a required due date (specific for each job). Aside from the main objectives, the output batches should also produce a balanced workload on the parallel machines, balanced job due dates within each batch, and minimal capacity loss in the batches. The scheduling problem also considers a batch capacity constraint, sequence-dependent processing times, incompatible product families, additional resources, and machine capability. We propose a two-phase heuristic approach that combines exact methods with search heuristics. The first phase comprises a four-stage mixed-integer linear program for building the batches; the second phase is based on a Greedy Randomized Adaptive Search Procedure for sequencing the batches assigned to each machine. We conducted experiments on instances with up to 100 jobs built with real data from the manufacturing facility. The results are encouraging both in terms of computing time—5 min in average—and quality of the solutions—less than 10 % relative gap from the optimal solution in the first phase and less than 5 % in the second phase. Additional experiments were conducted on randomly generated instances of small, medium, and large size.
      PubDate: 2014-12-01
  • Dynamic patient admission scheduling with operating room constraints,
           flexible horizons, and patient delays
    • Abstract: Abstract We revisit and extend the patient admission scheduling problem, in order to make it suitable for practical applications. The main novelty is that we consider constraints on the utilisation of operating rooms for patients requiring a surgery. In addition, we propose a more elaborate model that includes a flexible planning horizon, a complex notion of patient delay, and new components of the objective function. We design a solution approach based on local search, which explores the search space using a composite neighbourhood. In addition, we develop an instance generator that uses real-world data and statistical distributions so as to synthesise realistic and challenging case studies, which are made available on the web along with our solutions and the validator. Finally, we perform an extensive experimental evaluation of our solution method including statistically principled parameter tuning and an analysis of some features of the model and their corresponding impact on the objective function.
      PubDate: 2014-11-27
  • Temporal linear relaxation in IBM ILOG CP Optimizer
    • Abstract: Abstract IBM ILOG CP Optimizer is a constraint solver that implements a model-and-run paradigm. For scheduling problems, CP Optimizer provides a relatively simple but very expressive modeling language based on the notion of interval variables. This paper presents the temporal linear relaxation (TLR) used to guide the automatic search when solving scheduling problems that involve temporal and resource allocation costs. We give the rationale of the TLR, describe its integration in the automatic search of CP Optimizer, and present the relaxation of most of the constraints and expressions of the model. An experimental study on a set of classical scheduling benchmarks shows that using the TLR is essential for problems with irregular temporal costs and generally helps for problems with resource allocation costs.
      PubDate: 2014-11-25
  • Flowshop scheduling with interstage job transportation
    • Abstract: Abstract There are a variety of joint job production and transportation scheduling problems that arise in modern manufacturing systems. In this paper, we study two such problems that arise in a flowshop environment where there are two processing stages and a single transporter that is available to deliver the finished jobs from the first stage to the second. In the first problem, there is a single machine in each of the two flowshop stages and jobs have different sizes when loaded onto the transporter. In the second problem, there are two parallel machines in the first stage and a single machine in the second stage, and the transporter can carry only one job in each shipment. The objective of both problems is to minimize the makespan, i.e., the completion time of the last job in the second stage. The two problems are both strongly NP-hard. For each problem, we propose a fast heuristic and show that the heuristic has a tight worst-case bound of 2.
      PubDate: 2014-11-25
  • The Multi-Mode Resource-Constrained Multi-Project Scheduling Problem
    • Abstract: Abstract Scheduling projects is a difficult and time consuming process, and has far-reaching implications for any organization’s operations. By generalizing various aspects of project scheduling, decision makers are enabled to capture reality and act accordingly. In the context of the MISTA 2013 conference, the first MISTA challenge, organized by the authors, introduced such a general problem model: the Multi-Mode Resource-Constrained Multi-Project Scheduling Problem (MRCMPSP). The present paper reports on the competition and provides a discussion on its results. Furthermore, it provides an analysis of the submitted algorithms, and a study of their common elements. By making all benchmark datasets and results publicly available, further research on the MRCMPSP is stimulated.
      PubDate: 2014-11-22
  • A learning-based optimization approach to multi-project scheduling
    • Abstract: Abstract The present paper introduces a learning-based optimization approach to the resource-constrained multi-project scheduling problem. Multiple projects, each with their own set of activities, need to be scheduled. The objectives dealt with here include minimization of the average project delay and total makespan. The availability of local and global resources, precedence relations between activities, and non-equal project start times have to be considered. The proposed approach relies on a simple sequence learning game played by a group of project managers. The project managers each learn their activity list locally using reinforcement learning, more specifically learning automata. Meanwhile, they learn how to choose a suitable place in the overall sequence of all activity lists. All the projects need to arrive at a unique place in this sequence. A mediator, who usually has to solve a complex optimization problem, now manages a simple dispersion game. Through the mediator, a sequence of feasible activity lists is eventually scheduled by using a serial schedule generation scheme, which is adopted from single project scheduling. It is shown that the sequence learning approach has a large positive effect on minimizing the average project delay. In fact, the combination of local reinforcement learning, the sequence learning game and a forward-backward implementation of the serial scheduler significantly improves the best known results for all the MPSPLIB datasets. In addition, several new best results were obtained for both considered objectives: minimizing the average project delay and minimizing the total makespan.
      PubDate: 2014-11-04
  • The impact of core precedences in a cyclic RCPSP with precedence delays
    • Abstract: Abstract In this paper, we introduce a new kind of constraint, called a core precedence constraint, in a cyclic resource-constrained project scheduling problem (RCPSP) with precedence delays. We show, by an example, which kind of industrial constraints might be modeled by such core precedences in a periodic production setting. We then establish that these constraints can be quite easily added to an integer linear programming formulation of the cyclic RCPSP. Although core precedences seem to be very similar to classical precedence, they can induce infeasibility even without resource constraints. Moreover, we show that the feasibility checking problem is NP-complete in the strong sense, even assuming unit processing times and no resource constraints.
      PubDate: 2014-10-21
  • Optimal delivery time quotation in supply chains to minimize tardiness and
           delivery costs
    • Abstract: Abstract There are many situations when, due to unexpected delays, the supplier may not be able to deliver some orders by the promised due dates. We present a model for quoting attainable delivery times to minimize tardiness penalties and delivery costs, when deliveries take place in batches. We show that the general problem is strongly \({\mathcal {NP}}\) -hard, but when all orders have the same per-unit due-date-assignment cost, it is \({\mathcal {NP}}\) -hard only in the ordinary sense. For the latter case, we present a pseudo-polynomial algorithm, which is converted into a fully polynomial-time approximation scheme. If the tardiness penalties are also identical, we show that the problem can be solved in polynomial time.
      PubDate: 2014-10-21
  • Scheduling multi-colour print jobs with sequence-dependent setup times
    • Abstract: Abstract In this paper, a scheduling problem is considered which arises in the packaging industry. Plastic and foil wrappers used for packaging candy bars, crisps and other snacks typically require overlay printing with multiple colours. Printing machines used for this purpose usually accommodate a small number of colours which are loaded into a magazine simultaneously. If two consecutively scheduled print jobs require significantly different colour overlays, then substantial down times are incurred during the transition from the former magazine colour configuration to the latter, because ink cartridges corresponding to colours not required for the latter job have to be cleaned after completion of the former job. The durations of these down times are therefore sequence dependent (the washing and refilling time is a function of the number of colours in which two consecutive printing jobs differ). It is consequently desirable to schedule print jobs so that the accumulated down times associated with all magazine colour transitions are as short as possible for each printing machine. We show that an instance of this scheduling problem can be modelled as the well-known tool switching problem, which is tractable for small instances only. The problem can, however, be solved rather effectively in heuristic fashion by decomposing it into two subproblems: a job grouping problem (which can be modelled as a unicost set covering problem) and a group sequencing problem (which is a generalisation of the celebrated travelling salesman problem). We solve the colour print scheduling problem both exactly and heuristically for small, randomly generated test problem instances, studying the trade-off between the time efficiency and solution quality of the two approaches. Finally, we apply both solution approaches to real problem data obtained from a printing company in the South African Western Cape as a special case study.
      PubDate: 2014-10-15
  • A memetic algorithm to solve an unrelated parallel machine scheduling
           problem with auxiliary resources in semiconductor manufacturing
    • Abstract: Abstract In this paper, we propose a metaheuristic for solving an original scheduling problem with auxiliary resources in a photolithography workshop of a semiconductor plant. The photolithography workshop is often a bottleneck, and improving scheduling decisions in this workshop can help to improve indicators of the whole plant. Two optimization criteria are separately considered: the weighted flow time (to minimize) and the number of products that are processed (to maximize). After stating the problem and giving some properties on the solution space, we show how these properties help us to efficiently solve the problem with the proposed memetic algorithm, which has been implemented and tested on large generated instances. Numerical experiments show that good solutions are obtained within a reasonable computational time.
      PubDate: 2014-10-02
  • Interval scheduling and colorful independent sets
    • Abstract: Abstract Numerous applications in scheduling, such as resource allocation or steel manufacturing, can be modeled using the NP-hard Independent Set problem (given an undirected graph and an integer \(k\) , find a set of at least \(k\) pairwise non-adjacent vertices). Here, one encounters special graph classes like 2-union graphs (edge-wise unions of two interval graphs) and strip graphs (edge-wise unions of an interval graph and a cluster graph), on which Independent Set remains \(\mathrm{NP}\) -hard but admits constant ratio approximations in polynomial time. We study the parameterized complexity of Independent Set on 2-union graphs and on subclasses like strip graphs. Our investigations significantly benefit from a new structural “compactness” parameter of interval graphs and novel problem formulations using vertex-colored interval graphs. Our main contributions are as follows: We show a complexity dichotomy: restricted to graph classes closed under induced subgraphs and disjoint unions, Independent Set is polynomial-time solvable if both input interval graphs are cluster graphs, and is \(\mathrm{NP}\) -hard otherwise. We chart the possibilities and limits of effective polynomial-time preprocessing (also known as kernelization). We extend Halldórsson and Karlsson (2006)’s fixed-parameter algorithm for Independent Set on strip graphs parameterized by the structural parameter “maximum number of live jobs” to show that the problem (also known as Job Interval Selection) is fixed-parameter tractable with respect to the parameter \(k\) and generalize their algorithm from strip graphs to 2-union graphs. Preliminary experiments with random data indicate that Job Interval Selection with up to 15 jobs and \(5\cdot 10^5\) intervals can be solved optimally in less than 5 min.
      PubDate: 2014-10-02
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