Related papers: A Ptolemaic Partitioning Mechanism
In recent years, significant progress has been made on algorithms for learning optimal decision trees, primarily in the context of binary features. Extending these methods to continuous features remains substantially more challenging due to…
Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles,…
Herein, we investigate the zero-error randomized complexity, which is the least cost against the worst input, of AND-OR tree computation by imposing various restrictions on the algorithm to find the Boolean value of the root of that tree…
This paper presents a new probabilistic generative model for image segmentation, i.e. the task of partitioning an image into homogeneous regions. Our model is grounded on a mid-level image representation, called a region tree, in which…
Multi-task learning has gained popularity due to the advantages it provides with respect to resource usage and performance. Nonetheless, the joint optimization of parameters with respect to multiple tasks remains an active research topic.…
Classifying points in high dimensional spaces is a fundamental geometric problem in machine learning. In this paper, we address classifying points in the $d$-dimensional Hilbert polygonal metric. The Hilbert metric is a generalization of…
We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…
Rounding has proven to be a fundamental tool in theoretical computer science. By observing that rounding and partitioning of $\mathbb{R}^d$ are equivalent, we introduce the following natural partition problem which we call the {\em secluded…
We introduce a novel lower bound technique for distributed graph algorithms under bandwidth limitations. We define the notion of \emph{fooling views} and exemplify its strength by proving two new lower bounds for triangle membership in the…
We propose and analyze a two-level method for mimetic finite difference approximations of second order elliptic boundary value problems. We prove that the two-level algorithm is uniformly convergent, i.e., the number of iterations needed to…
With the increased use of machine learning systems for decision making, questions about the fairness properties of such systems start to take center stage. Most existing work on algorithmic fairness assume complete observation of features…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
We introduce a new heuristic for the A* algorithm that references a data structure much smaller than the one required by the ALT heuristic. This heuristic's benefits are permitted by a new approach for computing lower bounds using…
Employing a recently proposed separability criterion we develop analytical lower bounds for the concurrence and for the entanglement of formation of bipartite quantum systems. The separability criterion is based on a nondecomposable…
In this workshop, we discuss several algorithms for mathematical programs with equilibrium constraints (MPECs). The unifying theme is that MPECs are optimization problems whose feasible set contains a lower-level equilibrium system, often…
In multiobjective optimization, most branch and bound algorithms provide the decision maker with the whole Pareto front, and then decision maker could select a single solution finally. However, if the number of objectives is large, the…
Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…
In this paper, we present a new exact algorithm for counting perfect matchings, which relies on neither inclusion-exclusion principle nor tree-decompositions. For any bipartite graph of $2n$ nodes and $\Delta n$ edges such that $\Delta \geq…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…