Geometric inequalities for simplices which are the simplest and the most useful polytopes have been a very attractive subject for a long time. Mitrinovic, Pecaric, Volenec [9], Ali [1], Gerber [4], Petty, Waterman [11] and other authors [7,8] have obtained a great number of elegant results. Specially, the quantity relations involving two simplices have been studied extensively. The well-known N...

The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding techniques. We can avoid most DTW computations with an inexpensive lower bound (LB Keogh). We compare LB Keogh with a tighter lower bound (LB Improved). We find ...

, Finding a minimum weighted complete matching on a set of vertices in which the distances satisfy the triangle inequality is of general interest and of particular importance when drawing graphs on a mechanical plotter. The "greedy" heuristic of repeatedly matching the two closest unmatched points can be implemented in worst-case time O(n log n), a reasonable savings compared to the general min...

Network coordinates provide a mechanism for selecting and placing servers efficiently in a large distributed system. This approach works well as long as the coordinates continue to accurately reflect network topology. We conducted a long-term study of a subset of a million-plus node coordinate system and found that it exhibited some of the problems for which network coordinates are frequently c...

Hashing of databases is considered from the point of view of information and coding theory. The records of a database are represented as binary vectors of the same length stored in the external memory of a computer. The task is formulated as follows: given a pattern and a fixed size of working memory, form the set of addresses of records that can disagree with the pattern in the number of posit...

A number of similarity measures for comparing description logic concepts have been proposed. Criteria have been developed to evaluate a measure’s fitness for an application. These criteria include on the one hand those that ensure compatibility with the semantics, such as equivalence soundness, and on the other hand the properties of a metric, such as the triangle inequality. In this work we pr...

The asymmetric traveling salesman problem (ATSP) is one of the most fundamental problems in combinatorial optimization. An instance of ATSP is a directed complete graph G = (V,E) with edge weights w : E → N that satisfy the triangle inequality, i. e., w(a, c) ≤ w(a, b) +w(b, c) for all distinct vertices a, b, c ∈ V . The goal is to find a Hamiltonian cycle of minimum weight. The weight of a Ham...

Guruswami and Sinop [11] give a O(1/δ) approximation guarantee for the non-uniform Sparsest Cut problem by solving O(r)-level Lasserre semidefinite constraints, provided that the generalized eigenvalues of the Laplacians of the cost and demand graphs satisfy a certain spectral condition, namely, λr+1 ≥ Φ∗/(1 − δ). Their key idea is a rounding technique that first maps a vector-valued solution t...

The general asymmetric TSP with triangle inequality is known to be approximable only within an O(log n) factor, and is also known to be approximable within a constant factor as soon as the metric is bounded. In this paper we study the asymmetric and symmetric TSP problems with bounded metrics, i.e., metrics where the distances are integers between one and some upper bound B. We first prove appr...

Given a complete undirected graph with non negative costs on the edges the Edge Connected Subgraph Problem consists in nding the minimum cost spanning edge connected subgraph where multi edges are allowed in the solution A lower bound for the minimum cost edge connected subgraph is obtained by solving the linear programming relaxation for this problem which coincides with the subtour relaxation...