11 research outputs found
Capacitated max-Batching with Interval Graph Compatibilities
We consider the problem of partitioning interval graphs into cliques of bounded size. Each interval has a weight, and the cost of a clique is the maximum weight of any interval in the clique. This natural graph problem can be interpreted as a batch scheduling problem. Solving an open question from [7, 4, 5], we show NP-hardness, even if the bound on the clique sizes is constant. Moreover, we give a PTAS based on a novel dynamic programming technique for this case.
Heuristic algorithms for wireless mesh network planning
x, 131 leaves : ill. ; 29 cmTechnologies like IEEE 802.16j wireless mesh networks are drawing increasing attention of
the research community. Mesh networks are economically viable and may extend services
such as Internet to remote locations. This thesis takes interest into a planning problem in
IEEE 802.16j networks, where we need to establish minimum cost relay and base stations to
cover the bandwidth demand of wireless clients. A special feature of this planning problem
is that any node in this network can send data to at most one node towards the next hop,
thus traffic flow is unsplittable from source to destination.
We study different integer programming formulations of the problem. We propose four
types of heuristic algorithms that uses greedy, local search, variable neighborhood search
and Lagrangian relaxation based approaches for the problem. We evaluate the algorithms
on database of network instances of 500-5000 nodes, some of which are randomly generated
network instances, while other network instances are generated over geometric distribution.
Our experiments show that the proposed algorithms produce satisfactory result
compared to benchmarks produced by generalized optimization problem solver software
Algorithms for capacitated rectangle stabbing and lot-sizing with joint set-up costs
In the rectangle stabbing problem we are given a set of axis parallel rectangles and a set of horizontal and vertical lines, and our goal is to find a minimum size subset of lines that intersect all the rectangles. In this paper we study the capacitated version of this problem in which the input includes an integral capacity for each line. The capacity of a line bounds the number of rectangles that the line can cover. We consider two versions of this problem. In the first, one is allowed to use only a single copy of each line (hard capacities), and in the second, one is allowed to use multiple copies of every line, but the multiplicities are counted in the size (or weight) of the solution (soft capacities). We present an exact polynomial-time algorithm for the weighted one dimensional case with hard capacities that can be extended to the one dimensional weighted case with soft capacities. This algorithm is also extended to solve a certain capacitated multi-item lot sizing inventory problem with joint set-up costs. For the case of d-dimensional rectangle stabbing with soft capacities, we present a 3d-approximation algorithm for the unweighted case. For d-dimensional rectangle stabbing problem with hard capacities, we present a bi-criteria algorithm that computes 4d-approximate solutions that use at most two copies of every line. Finally, we present hardness results for rectangle stabbing when the dimension is part of the input and for a twodimensional weighted version with hard capacities
LIPIcs, Volume 258, SoCG 2023, Complete Volume
LIPIcs, Volume 258, SoCG 2023, Complete Volum
The benefits of an additional practice in descriptive geomerty course: non obligatory workshop at the Faculty of Civil Engineering in Belgrade
At the Faculty of Civil Engineering in Belgrade, in the Descriptive geometry (DG) course,
non-obligatory workshops named “facultative task” are held for the three generations of freshman
students with the aim to give students the opportunity to get higher final grade on the exam. The
content of this workshop was a creative task, performed by a group of three students, offering free
choice of a topic, i.e. the geometric structure associated with some real or imagery
architectural/art-work object.
After the workshops a questionnaire (composed by the professors at the course) is given to the
students, in order to get their response on teaching/learning materials for the DG course and the
workshop. During the workshop students performed one of the common tests for testing spatial
abilities, named “paper folding".
Based on the results of the questionnairethe investigation of the linkages between:students’
final achievements and spatial abilities, as well as students’ expectations of their performance on
the exam, and how the students’ capacity to correctly estimate their grades were associated with
expected and final grades, is provided. The goal was to give an evidence that a creative work,
performed by a small group of students and self-assessment of their performances are a good way
of helping students to maintain motivation and to accomplish their achievement.
The final conclusion is addressed to the benefits of additional workshops employment in the
course, which confirmhigherfinal scores-grades, achievement of creative results (facultative tasks)
and confirmation of DG knowledge adaption