5,345 research outputs found
Packing Sporadic Real-Time Tasks on Identical Multiprocessor Systems
In real-time systems, in addition to the functional correctness recurrent
tasks must fulfill timing constraints to ensure the correct behavior of the
system. Partitioned scheduling is widely used in real-time systems, i.e., the
tasks are statically assigned onto processors while ensuring that all timing
constraints are met. The decision version of the problem, which is to check
whether the deadline constraints of tasks can be satisfied on a given number of
identical processors, has been known -complete in the strong sense.
Several studies on this problem are based on approximations involving resource
augmentation, i.e., speeding up individual processors. This paper studies
another type of resource augmentation by allocating additional processors, a
topic that has not been explored until recently. We provide polynomial-time
algorithms and analysis, in which the approximation factors are dependent upon
the input instances. Specifically, the factors are related to the maximum ratio
of the period to the relative deadline of a task in the given task set. We also
show that these algorithms unfortunately cannot achieve a constant
approximation factor for general cases. Furthermore, we prove that the problem
does not admit any asymptotic polynomial-time approximation scheme (APTAS)
unless when the task set has constrained deadlines, i.e.,
the relative deadline of a task is no more than the period of the task.Comment: Accepted and to appear in ISAAC 2018, Yi-Lan, Taiwa
Closing the Gap for Pseudo-Polynomial Strip Packing
Two-dimensional packing problems are a fundamental class of optimization problems and Strip Packing is one of the most natural and famous among them. Indeed it can be defined in just one sentence: Given a set of rectangular axis parallel items and a strip with bounded width and infinite height, the objective is to find a packing of the items into the strip minimizing the packing height. We speak of pseudo-polynomial Strip Packing if we consider algorithms with pseudo-polynomial running time with respect to the width of the strip. It is known that there is no pseudo-polynomial time algorithm for Strip Packing with a ratio better than 5/4 unless P = NP. The best algorithm so far has a ratio of 4/3 + epsilon. In this paper, we close the gap between inapproximability result and currently known algorithms by presenting an algorithm with approximation ratio 5/4 + epsilon. The algorithm relies on a new structural result which is the main accomplishment of this paper. It states that each optimal solution can be transformed with bounded loss in the objective such that it has one of a polynomial number of different forms thus making the problem tractable by standard techniques, i.e., dynamic programming. To show the conceptual strength of the approach, we extend our result to other problems as well, e.g., Strip Packing with 90 degree rotations and Contiguous Moldable Task Scheduling, and present algorithms with approximation ratio 5/4 + epsilon for these problems as well
Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing
We study the Parallel Task Scheduling problem with a
constant number of machines. This problem is known to be strongly NP-complete
for each , while it is solvable in pseudo-polynomial time for each . We give a positive answer to the long-standing open question whether
this problem is strongly -complete for . As a second result, we
improve the lower bound of for approximating pseudo-polynomial
Strip Packing to . Since the best known approximation algorithm
for this problem has a ratio of , this result
narrows the gap between approximation ratio and inapproximability result by a
significant step. Both results are proven by a reduction from the strongly
-complete problem 3-Partition
Wireless Scheduling with Power Control
We consider the scheduling of arbitrary wireless links in the physical model
of interference to minimize the time for satisfying all requests. We study here
the combined problem of scheduling and power control, where we seek both an
assignment of power settings and a partition of the links so that each set
satisfies the signal-to-interference-plus-noise (SINR) constraints.
We give an algorithm that attains an approximation ratio of , where is the number of links and is the ratio
between the longest and the shortest link length. Under the natural assumption
that lengths are represented in binary, this gives the first approximation
ratio that is polylogarithmic in the size of the input. The algorithm has the
desirable property of using an oblivious power assignment, where the power
assigned to a sender depends only on the length of the link. We give evidence
that this dependence on is unavoidable, showing that any
reasonably-behaving oblivious power assignment results in a -approximation.
These results hold also for the (weighted) capacity problem of finding a
maximum (weighted) subset of links that can be scheduled in a single time slot.
In addition, we obtain improved approximation for a bidirectional variant of
the scheduling problem, give partial answers to questions about the utility of
graphs for modeling physical interference, and generalize the setting from the
standard 2-dimensional Euclidean plane to doubling metrics. Finally, we explore
the utility of graph models in capturing wireless interference.Comment: Revised full versio
Vector Bin Packing with Multiple-Choice
We consider a variant of bin packing called multiple-choice vector bin
packing. In this problem we are given a set of items, where each item can be
selected in one of several -dimensional incarnations. We are also given
bin types, each with its own cost and -dimensional size. Our goal is to pack
the items in a set of bins of minimum overall cost. The problem is motivated by
scheduling in networks with guaranteed quality of service (QoS), but due to its
general formulation it has many other applications as well. We present an
approximation algorithm that is guaranteed to produce a solution whose cost is
about times the optimum. For the running time to be polynomial we
require and . This extends previous results for vector
bin packing, in which each item has a single incarnation and there is only one
bin type. To obtain our result we also present a PTAS for the multiple-choice
version of multidimensional knapsack, where we are given only one bin and the
goal is to pack a maximum weight set of (incarnations of) items in that bin
Dagstuhl Reports : Volume 1, Issue 2, February 2011
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
- …