Polyhedral Approaches to Hypergraph Partitioning and Cell Formation
Author(s)
Advisor
Akgül, MustafaDate
1994Publisher
Bilkent University
Language
English
Type
ThesisItem Usage Stats
186
views
views
386
downloads
downloads
Abstract
Hypergraphs are generalizations of graphs in the sense that each hyperedge
can connect more than two vertices. Hypergraphs are used to describe manufacturing
environments and electrical circuits. Hypergraph partitioning in manufacturing
models cell formation in Cellular Manufacturing systems. Moreover,
hypergraph partitioning in VTSI design case is necessary to simplify the layout
problem. There are various heuristic techniques for obtaining non-optimal hypergraph
partitionings reported in the literature. In this dissertation research,
optimal seeking hypergraph partitioning approaches are attacked from polyhedral
combinatorics viewpoint.
There are two polytopes defined on r-uniform hypergraphs in which every
hyperedge has exactly r end points, in order to analyze partitioning related problems.
Their dimensions, valid inequality families, facet defining inequalities are
investigated, and experimented via random test problems.
Cell formation is the first stage in designing Cellular Manufacturing systems.
There are two new cell formation techniques based on combinatorial optimization
principles. One uses graph approximation, creation of a flow equivalent tree by
successively solving maximum flow problems and a search routine. The other
uses the polynomially solvable special case of the one of the previously discussed
polytopes. These new techniques are compared to six well-known cell formation
algorithms in terms of different efficiency measures according to randomly generated
problems. The results are analyzed statistically.
Keywords
Combinatorial optimizationPolyhedral combinatorics
Hypergraph partitioning
Cellular manufacturing systems