Related papers: A Ptolemaic Partitioning Mechanism
Most research into similarity search in metric spaces relies upon the triangle inequality property. This property allows the space to be arranged according to relative distances to avoid searching some subspaces. We show that many common…
This paper discusses a new family of bounds for use in similarity search, related to those used in metric indexing, but based on Ptolemy's inequality, rather than the metric axioms. Ptolemy's inequality holds for the well-known Euclidean…
Metric search is concerned with the efficient evaluation of queries in metric spaces. In general,a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query…
Ptolemy's inequality is a classic relationship between the distances among four points in Euclidean space. Another relationship between six distances is the 4-point condition, an inequality satisfied by the lengths of the six paths that…
We introduce a new heuristic for the A* algorithm that references a data structure significantly smaller than that of ALT. We characterize the behavior of this new heuristic based on a dual landmark configuration that leverages…
Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
We present linear-time algorithms for partitioning a path or a tree with weights on the vertices by removing $k$ edges to maximize the minimum-weight component. We also use the same framework to partition a path with weight on the vertices,…
We develop numerical methods for elliptic systems governed by partial segregation constraints, in which three nonnegative components are required to have a vanishing pointwise product throughout the domain. This constraint enforces that at…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…
Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible…
A new 1D search method is proposed for minimizing an arbitrary real valued function. The algorithm is a modification of the interval halving method which is based on dividing the interval of uncertainty by three points into four equal…
Machine learning algorithms aim at minimizing the number of false decisions and increasing the accuracy of predictions. However, the high predictive power of advanced algorithms comes at the costs of transparency. State-of-the-art methods,…
Alternative novel measures of the distance between any two partitions of a n-set are proposed and compared, together with a main existing one, namely 'partition-distance' D(.,.). The comparison achieves by checking their restriction to…
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges…
Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and nonconvex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction…
Divide and Conquer is a well known algorithmic procedure for solving many kinds of problem. In this procedure, the problem is partitioned into two parts until the problem is trivially solvable. Finding the distance of the closest pair is an…
This paper presents an improved forward-backward splitting algorithm with two inertial parameters. It aims to find a point in the real Hilbert space at which the sum of a co-coercive operator and a maximal monotone operator vanishes. Under…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
A novel algorithm is proposed for segmenting an image into multiple levels using its mean and variance. Starting from the extreme pixel values at both ends of the histogram plot, the algorithm is applied recursively on sub-ranges computed…