16 research outputs found
Some complexity and approximation results for coupled-tasks scheduling problem according to topology
We consider the makespan minimization coupled-tasks problem in presence of
compatibility constraints with a specified topology. In particular, we focus on
stretched coupled-tasks, i.e. coupled-tasks having the same sub-tasks execution
time and idle time duration. We study several problems in framework of classic
complexity and approximation for which the compatibility graph is bipartite
(star, chain,. . .). In such a context, we design some efficient
polynomial-time approximation algorithms for an intractable scheduling problem
according to some parameters
Scheduling periodic messages on a shared link
Cloud-RAN is a recent architecture for mobile networks where the processing
units are located in distant data centers while, until now, they were attached
to antennas. The main challenge, to fulfill protocol constraints, is to
guarantee low latency for the periodic messages sent from each antenna to its
processing unit and back. The problem we address is to find a periodic sending
scheme of these messages \emph{without contention nor buffering}, when all
messages are of the same size and the period is fixed.
We study the periodic message assignment problem modeling this situation on a
common topology, where contention arises from a single link shared by all
antennas. The problem is reminiscent of coupled-task scheduling, but the
periodicity introduces a new twist. We study how the problem behaves with
regard to the \emph{load} of the shared link. The main contributions are
polynomial-time algorithms which \emph{always} find a solution for an arbitrary
size of messages and load at most or for messages of size one and load at
most , the golden ratio conjugate. We also prove that a randomized
greedy algorithm finds a solution on almost all instances with high
probability, explaining why most greedy algorithms work so well in practice.Comment: 23 pages, 18 figure
Parameterized Complexity of a Parallel Machine Scheduling Problem
In this paper we consider the parameterized complexity of two versions of a parallel machine scheduling problem with precedence delays, unit processing times and time windows. In the first version - with exact delays - we assume that the delay between two jobs must be exactly respected, whereas in the second version - with minimum delays - the delay between two jobs is a lower bound on the time between them. Two parameters are considered for this analysis: the pathwidth of the interval graph induced by the time windows and the maximum precedence delay value. We prove that our problems are para-NP-complete with respect to any of the two parameters and fixed-parameter tractable parameterized by the pair of parameters
Cable Tree Wiring -- Benchmarking Solvers on a Real-World Scheduling Problem with a Variety of Precedence Constraints
Cable trees are used in industrial products to transmit energy and
information between different product parts. To this date, they are mostly
assembled by humans and only few automated manufacturing solutions exist using
complex robotic machines. For these machines, the wiring plan has to be
translated into a wiring sequence of cable plugging operations to be followed
by the machine. In this paper, we study and formalize the problem of deriving
the optimal wiring sequence for a given layout of a cable tree. We summarize
our investigations to model this cable tree wiring Problem (CTW) as a traveling
salesman problem with atomic, soft atomic, and disjunctive precedence
constraints as well as tour-dependent edge costs such that it can be solved by
state-of-the-art constraint programming (CP), Optimization Modulo Theories
(OMT), and mixed-integer programming (MIP) solvers. It is further shown, how
the CTW problem can be viewed as a soft version of the coupled tasks scheduling
problem. We discuss various modeling variants for the problem, prove its
NP-hardness, and empirically compare CP, OMT, and MIP solvers on a benchmark
set of 278 instances. The complete benchmark set with all models and instance
data is available on github and is accepted for inclusion in the MiniZinc
challenge 2020