188 research outputs found
Parameterized complexity of machine scheduling: 15 open problems
Machine scheduling problems are a long-time key domain of algorithms and
complexity research. A novel approach to machine scheduling problems are
fixed-parameter algorithms. To stimulate this thriving research direction, we
propose 15 open questions in this area whose resolution we expect to lead to
the discovery of new approaches and techniques both in scheduling and
parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc
On strongly polynomial algorithms for some classes of quadratic programming problems
In this paper we survey some results concerning polynomial and/or
strongly polynomial solvability of some classes of quadratic programming problems.
The discussion on polynomial solvability of continuous convex quadratic programming is followed by a couple of models for
quadratic integer programming which, due to their special structure, allow polynomial (or even strongly polynomial) solvability. The theoretical merit of those results stems from the fact that a
running time (i.e. the number of elementary arithmetic operations) of a strongly polynomial algorithm is independent of the input size of the problem
04231 Abstracts Collection -- Scheduling in Computer and Manufacturing Systems
During 31.05.-04.06.04, the Dagstuhl Seminar 04231 "Scheduling in Computer and Manufacturing Systems" 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
Polynomiality for Bin Packing with a Constant Number of Item Types
We consider the bin packing problem with d different item sizes s_i and item
multiplicities a_i, where all numbers are given in binary encoding. This
problem formulation is also known as the 1-dimensional cutting stock problem.
In this work, we provide an algorithm which, for constant d, solves bin
packing in polynomial time. This was an open problem for all d >= 3.
In fact, for constant d our algorithm solves the following problem in
polynomial time: given two d-dimensional polytopes P and Q, find the smallest
number of integer points in P whose sum lies in Q.
Our approach also applies to high multiplicity scheduling problems in which
the number of copies of each job type is given in binary encoding and each type
comes with certain parameters such as release dates, processing times and
deadlines. We show that a variety of high multiplicity scheduling problems can
be solved in polynomial time if the number of job types is constant
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