5 research outputs found
Scheduling under Linear Constraints
We introduce a parallel machine scheduling problem in which the processing
times of jobs are not given in advance but are determined by a system of linear
constraints. The objective is to minimize the makespan, i.e., the maximum job
completion time among all feasible choices. This novel problem is motivated by
various real-world application scenarios. We discuss the computational
complexity and algorithms for various settings of this problem. In particular,
we show that if there is only one machine with an arbitrary number of linear
constraints, or there is an arbitrary number of machines with no more than two
linear constraints, or both the number of machines and the number of linear
constraints are fixed constants, then the problem is polynomial-time solvable
via solving a series of linear programming problems. If both the number of
machines and the number of constraints are inputs of the problem instance, then
the problem is NP-Hard. We further propose several approximation algorithms for
the latter case.Comment: 21 page
The robust single machine scheduling problem with uncertain release and processing times
In this work, we study the single machine scheduling problem with uncertain
release times and processing times of jobs. We adopt a robust scheduling
approach, in which the measure of robustness to be minimized for a given
sequence of jobs is the worst-case objective function value from the set of all
possible realizations of release and processing times. The objective function
value is the total flow time of all jobs. We discuss some important properties
of robust schedules for zero and non-zero release times, and illustrate the
added complexity in robust scheduling given non-zero release times. We propose
heuristics based on variable neighborhood search and iterated local search to
solve the problem and generate robust schedules. The algorithms are tested and
their solution performance is compared with optimal solutions or lower bounds
through numerical experiments based on synthetic data
Database query optimisation based on measures of regret
The query optimiser in a database management system (DBMS) is responsible for
�nding a good order in which to execute the operators in a given query. However, in
practice the query optimiser does not usually guarantee to �nd the best plan. This is
often due to the non-availability of precise statistical data or inaccurate assumptions
made by the optimiser. In this thesis we propose a robust approach to logical query
optimisation that takes into account the unreliability in database statistics during
the optimisation process. In particular, we study the ordering problem for selection
operators and for join operators, where selectivities are modelled as intervals rather
than exact values. As a measure of optimality, we use a concept from decision theory
called minmax regret optimisation (MRO).
When using interval selectivities, the decision problem for selection operator ordering
turns out to be NP-hard. After investigating properties of the problem and
identifying special cases which can be solved in polynomial time, we develop a novel
heuristic for solving the general selection ordering problem in polynomial time. Experimental
evaluation of the heuristic using synthetic data, the Star Schema Benchmark
and real-world data sets shows that it outperforms other heuristics (which take
an optimistic, pessimistic or midpoint approach) and also produces plans whose regret
is on average very close to optimal.
The general join ordering problem is known to be NP-hard, even for exact selectivities.
So, for interval selectivities, we restrict our investigation to sets of join
operators which form a chain and to plans that correspond to left-deep join trees.
We investigate properties of the problem and use these, along with ideas from the
selection ordering heuristic and other algorithms in the literature, to develop a
polynomial-time heuristic tailored for the join ordering problem. Experimental evaluation
of the heuristic shows that, once again, it performs better than the optimistic,
pessimistic and midpoint heuristics. In addition, the results show that the heuristic
produces plans whose regret is on average even closer to the optimal than for
selection ordering