2,021 research outputs found
Approximation Algorithms for Scheduling with Resource and Precedence Constraints
We study non-preemptive scheduling problems on identical parallel machines and uniformly related machines under both resource constraints and general precedence constraints between jobs. Our first result is an O(logn)-approximation algorithm for the objective of minimizing the makespan on parallel identical machines under resource and general precedence constraints. We then use this result as a subroutine to obtain an O(logn)-approximation algorithm for the
more general objective of minimizing the total weighted completion time on parallel identical machines under both constraints. Finally, we present an O(logm logn)-approximation algorithm for scheduling under these constraints on uniformly related machines. We show that these results can all be generalized to include the case where each job has a release time. This is the first upper bound on the approximability of this class of scheduling problems where both resource and general precedence constraints must be satisfied simultaneously
08071 Abstracts Collection -- Scheduling
From 10.02. to 15.02., the Dagstuhl Seminar 08071 ``Scheduling\u27\u27 was held
in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Approximation Algorithms for Scheduling Parallel Jobs: Breaking the Approximation Ratio of 2
In this paper we study variants of the non-preemptive parallel job scheduling problem in which the number of machines is polynomially bounded in the number of jobs. For this problem we show that a schedule with length at most (1 + Δ)OPT can be calculated in polynomial time. Unless P = NP, this is the best possible result (in the sense of approximation ratio), since the problem is strongly NP-hard. For the case, where all jobs must be allotted to a subset of consecutive machines, a schedule with length at most (1.5 + Δ)OPT can be calculated in polynomial time. The previously best known results are algorithms with absolute approximation ratio 2. Furthermore, we extend both algorithms to the case of malleable jobs with the same approximation ratios
Approximation algorithms for scheduling and two-dimensional packing problems
This dissertation thesis is concerned with two topics of combinatorial optimization : scheduling and geometrical packing problems. Scheduling deals with the assignment of jobs to machines in a âgoodâ way, for suitable notions of good. Two particular problems are studied in depth : on the one hand, we consider the impact of machine failure on online scheduling, i.e. what are the consequences of the fact that in real life, machines do not work flawlessly around the clock, but need maintenance intervals or can break down? How do we need to adapt our algorithms to still obtain good overall schedules, and in what settings do we even have a chance to succeed? Our second problem is of a more static nature : in some settings, not every job is permitted on all the machines. A classical example would be that of workers which needs special qualification to execute some jobs, or a certain minimum requirement of memory size of computers, etc. The problem in general is notoriously hard to tackle; we present improved approximation ratios for several special cases. In particular, we derive a polynomial-time approximation scheme for nested interval restrictions, which occur naturally in many practical applications. Our final topic is two-dimensional geometric bin packing, the problem of packing rectangular objects into the minimum number of containers of identical size (figuratively speaking, we are arranging advertisements of fixed dimensions into the minimum number of print pages). It is known that no approximation ratio better than 2 is possible for this problem, unless P = NP; we present an algorithm that guarantees this ratio.Diese Promotionsschrift behandelt zwei Arten kombinatorischer Optimierungsprobleme : Ablaufplanungsprobleme und geometrische Packungsprobleme. Ablaufplanungsprobleme handeln davon, eine Menge von Aufgaben, die Jobs, auf eine Menge von ausfĂŒhrenden Maschinen oder Arbeitern zu verteilen, so dass
der entstehende Ablaufplan in geeignetem Sinne gut ist. Wir betrachten hier insbesondere folgende zwei Probleme der Ablaufplanung: einerseits untersuchen wir den Einfluà von MaschinenausfÀllen auf die Online-Ablaufplanung: im wirklichen Leben sind Maschinen nicht fehler- und
unterbrechungslos verfĂŒgbar. Wir geben eine teilweise Antwort auf die Frage, mit welchen Ănderungen Algorithmen trotz unerwartet auftretender MaschinenausfĂ€lle gute PlĂ€ne erstellen können, und in welchen FĂ€llen es prinzipiell nicht möglich ist, gute AblaufplĂ€ne zu erstellen. Unser zweites Ablaufplanungsproblem ist von statischerer Natur: in der
praktischen Anwendung ist es hĂ€ufig der Fall, dass nicht jede Maschine jeden Job ausfĂŒhren kann. Ein einfaches Beispiel sind menschliche Arbeiter, die gewisse formale Qualifikationen fĂŒr gewisse Jobs haben mĂŒssen. Diese Problem
erweist sich als in voller Allgemeinheit bekannt hartnĂ€ckig; wir stellen hier Algorithmen fĂŒr einige SpezialfĂ€lle vor. Insbesondere prĂ€sentieren wir ein polynomielles Approximationsschema fĂŒr den wichtigen Fall verschachtelter Restriktionen, der in der Mitarbeiterplanung auf natĂŒrliche
Weise auftritt. Schlussendlich untersuchen wir das zweidimensionale geometrische bin packing-Problem. Fragestellung dieses Problem ist es, rechteckige Objekte
in die minimale Anzahl von Containern gleicher GröĂe zu packen. Salopp gesprochen versuchen wir, eine vorgegebene Menge von Anzeigen mit vorgegebenen Abmessungen auf eine möglichst kleine Zahl von Druckseiten gleicher GröĂe zu platzieren. Es ist bekannt, dass dieses Problem keine
Algorithmus mit ApproximationsgĂŒte besser als 2 erlaubt, es sei denn, P = NP; wir stellen einen Algorithmus mit GĂŒte 2 vor
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