# Donna Crystal Llewellyn

• Discrete Applied Mathematics
• 1989
We recently noticed an error in our paper, “Local optimization on graphs”, which appeared in volume 23, 1989, pages 157-178, of Discrete Applied Mathematics. The error is not too serious, in that all of the lemmata, propositions, and theorems are correct as given. However, the divide-and-conquer algorithm in Section 2.1, p. 159, is incomplete. The necessary(More)
• Discrete Mathematics
• 2001
Matching 2-lattice polyhedra are a special class of lattice polyhedra that include network 3ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, etc. In this paper we develop a polynomial-time extreme point algorithm for #nding a maximum cardinality vector in a matching 2-lattice polyhedron. c © 2001 Elsevier Science B.V. All rights(More)
• Discrete Mathematics
• 2001
Two-lattice polyhedra are a special class of lattice polyhedra that include network 4ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, the intersection of two polymatroids, etc. In this paper we show that the maximum sum of components of a vector in a 2-lattice polyhedron is equal to the minimum capacity of a cover for the(More)
• Discrete Applied Mathematics
• 1993
Llewellyn, D.C. and C.A. Tovey, Dividing and conquering the square, Discrete Applied Mathematics 43 (1993) 131~153. A local minimum of a matrix is a cell whose value is smaller than those of its four adjacent cells. For an n x n square matrix, we find a local minimum with at most 2.554~ queries, and prove a lower bound of 4% queries required by any method.(More)
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• Min algebra has been used (Cuninghame-Greem [2], Hoffman [3]) to obtain results in operations research and graph theory. It has previously been seen primarily as an efficient way to describe a system of minimum relations. In this note we develop an elimination scheme for inductively solving systems of min algebraic equations and then prove a theorem of the(More)
This is the first in a series of papers that explores a class of polyhedra we call 2-lattice polyhedra. 2-Lattice polyhedra are a special class of lattice polyhedra that include network flow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, the intersection of two polymatroids, etc. In this paper we show that the maximum sum of(More)
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