Unit Distance Problems

Points at Rational Distance from the Vertices of a Unit Polygon

Optimization Problems over Unit-Distance Representations of Graphs

We study the relationship between unit-distance representations and the Lovász theta number of graphs, originally established by Lovász. We derive and prove min-max theorems. This framework allows us to derive a weighted version of the hypersphere number of a graph and a related min-max theorem. Then, we connect to sandwich theorems via graph homomorphisms. We present and study a generalization...

Single facility location problems with unbounded unit balls

In this paper we consider a new class of continuous location problems where the ''distances'' are measured by gauges of closed (not necessarily bounded) convex sets. These distance functions do not satisfy the definiteness property and therefore they can be used to model those situations where there exist zero-distance regions. We prove a geometrical characterization of these measures of distan...

Data Envelopment Analysis, Genetic Algorithm, Hyperplane, Efficient Unit

Data Envelopment Analysis (DEA) is actually to obtain the efficiency using inputs and outputs, which can determine efficient and inefficient units with the help of performance calculations such that the efficiency for efficient DMUs is one and less than one for inefficient DMUs [1]. In some cases, the ranking of the decision-making units are not important for decision-makers, and they are only ...

Local solutions for global problems in wireless networks

In this paper, we review a recently developed class of algorithms that solve global problems in unit distance wireless networks by means of local algorithms. A local algorithm is one in which any node of a network only has information on nodes at distance at most k from itself, for a constant k. For example, given a unit distance wireless network N , we want to obtain a planar subnetwork of N b...

Improvement Least-Distance Measure Model with Coplanar DMU on Strong Hyperplanes

Technique of Data Envelopment Analysis (DEA) involves methods conducted for desirable objective management of Decision Making Unit (DMU) that is same increasing of efficiency level. Data envelopment analysis furthermore determines the efficiency level, provides situation, removes inefficiency with evaluated benchmarking information. In this paper the use of the improvement Least-Distance me...