Multi-Criteria Flow-Shop Scheduling Optimization

A flow-shop is a type of manufacturing job shop where similar jobs follow a similar, linear sequence through the shop. Every day, flow-shops receive several different orders and it is up to the scheduler to plan the daily schedule. This schedule should be designed to prevent bottlenecks in the shop, to have on-time delivery of products, and satisfy several other requirements. Often, schedulers perform subjective scheduling and utilize simple heuristics or just intuition to schedule the jobs. With computer-based scheduling, schedulers can now create schedules and determine quantitatively what sorts of schedules work best. Currently, much of the computer-based schedules only try to optimize for one KPI such as Total Tardiness. This paper considers incorporating multiple-criteria into computer based scheduling so that schedulers can have more flexibility and develop schedules which optimize multiple-criteria; this paper specifically considers minimizing Total Tardiness and maximizing Throughput. Comparisons between single-criterion models and the multiple-criteria model are made and it is discovered the multiple-criteria model provides a great compromise in optimizing both KPIs. A user-friendly program is developed where schedulers of any flow-shop can utilize the software to compute schedules for cases up to 10 jobs and 10 machines

Realizing degree sequences in parallel

A sequence $d$ of integers is a degree sequence if there exists a (simple) graph $G$ such that the components of $d$ are equal to the degrees of the vertices of $G$. The graph $G$ is said to be a realization of $d$. We provide an efficient parallel algorithm to realize $d$. Before our result, it was not known if the problem of realizing $d$ is in $NC$

All-pairs min-cut in sparse networks

Algorithms are presented for the all-pairs min-cut problem in bounded tree-width, planar and sparse networks. The approach used is to preprocess the input $n$-vertex network so that, afterwards, the value of a min-cut between any two vertices can be efficiently computed. A tradeoff is shown between the preprocessing time and the time taken to compute min-cuts subsequently. In particular, after an $O(n\log n)$ preprocessing of a bounded tree-width network, it is possible to find the value of a min-cut between any two vertices in constant time. This implies that for such networks the all-pairs min-cut problem can be solved in time $O(n^2)$. This algorithm is used in conjunction with a graph decomposition technique of Frederickson to obtain algorithms for sparse and planar networks. The running times depend upon a topological property, $\gamma$, of the input network. The parameter $\gamma$ varies between 1 and $\Theta(n)$; the algorithms perform well when $\gamma = o(n)$. The value of a min-cut can be found in time $O(n + \gamma^2 \log \gamma)$ and all-pairs min-cut can be solved in time $O(n^2 + \gamma^4 \log \gamma)$ for sparse networks. The corresponding running times4 for planar networks are $O(n+\gamma \log \gamma)$ and $O(n^2 + \gamma^3 \log \gamma)$, respectively. The latter bounds depend on a result of independent interest: outerplanar networks have small ``mimicking'' networks which are also outerplanar

On the parallel complexity of degree sequence problems

We describe a robust and efficient implementation of the Bentley-Ottmann sweep line algorithm based on the LEDA library of efficient data types and algorithms. The program computes the planar graph $G$ induced by a set $S$ of straight line segments in the plane. The nodes of $G$ are all endpoints and all proper intersection points of segments in $S$. The edges of $G$ are the maximal relatively open subsegments of segments in $S$ that contain no node of $G$. All edges are directed from left to right or upwards. The algorithm runs in time $O((n+s) log n)$ where $n$ is the number of segments and $s$ is the number of vertices of the graph $G$. The implementation uses exact arithmetic for the reliable realization of the geometric primitives and it uses floating point filters to reduce the overhead of exact arithmetic

All-Pairs Min-Cut in Sparse Networks

Algorithms are presented for the all-pairs min-cut problem in bounded treewidth, planar, and sparse networks. The approach used is to preprocess the input n-vertex network so that afterward, the value of a min-cut between any two vertices can be efficiently computed. A tradeoff is shown between the preprocessing time and the time taken to compute min-cuts subsequently. In particular, after an Onlog Ž n. preprocessing of a bounded tree-width network, it is possible to find the value of a min-cut between any two vertices in constant time. This implies that for Ž 2 such networks the all-pairs min-cut problem can be solved in time On.. This algorithm is used in conjunction with a graph decomposition technique of Frederickson to obtain algorithms for sparse and planar networks. The running times depend upon a topological property, �, of the input network. The parameter � varies between 1 and �Ž. n; the algorithms perform well when � � on. Ž. The value Ž 2 of a min-cut can be found in time On� � log �. and all-pairs min-cut can be Ž 2 4 solved in time On � � log �. for sparse networks. The corresponding runnin

Near-Linear-Time Deterministic Plane Steiner Spanners and TSP Approximation for Well-Spaced Point Sets

We describe an algorithm that takes as input n points in the plane and a parameter {\epsilon}, and produces as output an embedded planar graph having the given points as a subset of its vertices in which the graph distances are a (1 + {\epsilon})-approximation to the geometric distances between the given points. For point sets in which the Delaunay triangulation has bounded sharpest angle, our algorithm's output has O(n) vertices, its weight is O(1) times the minimum spanning tree weight, and the algorithm's running time is bounded by O(n \sqrt{log log n}). We use this result in a similarly fast deterministic approximation scheme for the traveling salesperson problem.Comment: Appear at the 24th Canadian Conference on Computational Geometry. To appear in CGT

Approximation Algorithms for Maximum Two-Dimensional Pattern Matching

Dessmark y Andrzej Lingas z Madhav V. Marathe

New results in algorithmic graph theory.

New results in algorithmic graph theory