Concepts inApproximating TSP on metrics with bounded global growth
Travelling salesman problem
The travelling salesman problem (TSP) is an NP-hard problem in combinatorial optimization studied in operations research and theoretical computer science. Given a list of cities and their pairwise distances, the task is to find the shortest possible route that visits each city exactly once and returns to the origin city. It is a special case of the travelling purchaser problem.
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Metric (mathematics)
In mathematics, a metric or distance function is a function which defines a distance between elements of a set. A set with a metric is called a metric space. A metric induces a topology on a set but not all topologies can be generated by a metric. A topological space whose topology can be described by a metric is called metrizable.
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SNP (complexity)
In computational complexity theory, SNP (from Strict NP) is a complexity class containing a limited subset of NP based on its logical characterization in terms of graph-theoretical properties. It forms the basis for the definition of the class MaxSNP of optimization problems.
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Correlation dimension
In chaos theory, the correlation dimension (denoted by ¿) is a measure of the dimensionality of the space occupied by a set of random points, often referred to as a type of fractal dimension. For example, if we have a set of random points on the real number line between 0 and 1, the correlation dimension will be ¿ = 1, while if they are distributed on say, a triangle embedded in three-dimensional space (or m-dimensional space), the correlation dimension will be ¿ = 2.
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Metric dimension (graph theory)
In graph theory, the metric dimension of a graph G is the minimum number of vertices in a subset S of G such that all other vertices are uniquely determined by their distances to the vertices in S. Finding the metric dimension of a graph is an NP-hard problem; the decision version, determining whether the metric dimension is less than a given value, is NP-complete.
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Well-behaved
Mathematicians (and those in related sciences) very frequently speak of whether a mathematical object¿a function, a set, a space of one sort or another¿is "well-behaved". The term has no fixed formal definition, and is dependent on mathematical interests, fashion, and taste. To ensure that an object is "well-behaved" mathematicians introduce further axioms to narrow down the domain of study.
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NP-complete
In computational complexity theory, the complexity class NP-complete (abbreviated NP-C or NPC) is a class of decision problems. A decision problem L is NP-complete if it is in the set of NP problems so that any given solution to the decision problem can be verified in polynomial time, and also in the set of NP-hard problems so that any NP problem can be converted into L by a transformation of the inputs in polynomial time.
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Metric space
In mathematics, a metric space is a set where a notion of distance between elements of the set is defined. The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance.
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