In computational geometry, packing problems ask whether a set of rigid pieces can be placed inside a target region such that no two pieces overlap. The triangle packing problem is a packing problem that involves triangular pieces, and it is crucial for algorithm design in many areas, including origami design, cutting industries, and warehousing. Previous works in packing algorithms have conject...

We show that the problem of deciding whether a digraph has a Hamiltonian path between two specified vertices and the problem of deciding whether a given graph has a cubic subgraph are complete for monotone NP via monotone projection translations. We also show that the problem of deciding whether a uniquely partially orderable (resp. comparability) graph has a cubic subgraph is complete for NP v...

Preplaced circuit modules may be rotated to improve performance and/or routability. We show that several simple versions of the module rotation problem are NP-hard.

We show that the problems of approximating the shortest and closest vector in a lattice to within a factor of √ n lie in NP intersect coNP. The result (almost) subsumes the three mutually-incomparable previous results regarding these lattice problems: Banaszczyk [7], Goldreich and Goldwasser [14], and Aharonov and Regev [2]. Our technique is based on a simple fact regarding succinct approximati...

This paper concerns the complexity analysis of the roommate problem and intern assignment problem with couples. These are two special cases of the matching problems known as stable matching. The roommate problem is that of assigning a set of people to rooms of exactly two occupants in accordance with the preferences of the members of the set. The intern assignment problem with couples is that o...

University of Florida Technical Report 91-29 Abstract Graphs with delays associated with their edges are often used to model communication and signal flow networks. Network performance can be improved by upgrading the network vertices. Such an improvement reduces the edge delays and comes at a cost. We study different formulations of this network performance improvement problem and show that th...

We consider the problem of identifying n points in the plane using disks, i.e., minimizing the number of disks so that each point is contained in a disk and no two points are in exactly the same set of disks. This problem can be seen as an instance of the test covering problem with geometric constraints on the tests. We give tight lower and upper bounds on the number of disks needed to identify...

Abstract An E -fuzzy group is a lattice-valued algebraic structure, defined on a crisp algebra which is not necessarily a group. The crisp equality is replaced by a particular fuzzy one denoted by E . Classical group-like properties are formulated as appropriate fuzzy identities special lattice theoretic formulas. We prove basic features of E -fuzzy groups: properties of the unit and inverses, ...