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In 2016, Chandrasekaran, V\'egh, and Vempala published a method to solve the minimum-cost perfect matching problem on an arbitrary graph by solving a strictly polynomial number of linear programs. However, their method requires a strong…

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…

Similar to many Machine Learning models, both accuracy and speed of the Cluster weighted models (CWMs) can be hampered by high-dimensional data, leading to previous works on a parsimonious technique to reduce the effect of "Curse of…

This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…

This paper presents a generalization of the "weighted least-squares" (WLS), named "weighted pairing least-squares" (WPLS), which uses a rectangular weight matrix and is suitable for data alignment problems. Two fast solving methods,…

We describe our methodology for comparing the WMAP measurements of the cosmic microwave background (CMB) and other complementary data sets to theoretical models. The unprecedented quality of the WMAP data, and the tight constraints on…

Cycle packing is a fundamental problem in optimization, graph theory, and algorithms. Motivated by recent advancements in finding vertex-disjoint paths between a specified set of vertices that either minimize the total length of the paths…

In this paper, we propose a machine learning model for sparse pairwise comparison matrices (PCMs), combining classical PCM approaches with graph-based learning techniques. Numerical results are provided to demonstrate the effectiveness and…

We present a space and time efficient practical parallel algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. The core of the algorithm is a…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

Python implementation of selected weighted graph algorithms is presented. The minimal graph interface is defined together with several classes implementing this interface. Graph nodes can be any hashable Python objects. Directed edges are…

Quantifying the contributions, or weights, of comparisons or single studies to the estimates in a network meta-analysis (NMA) is an active area of research. We extend this to the contributions of paths to NMA estimates. We present a general…

In parameter estimation problems one computes a posterior distribution over uncertain parameters defined jointly by a prior distribution, a model, and noisy data. Markov Chain Monte Carlo (MCMC) is often used for the numerical solution of…

Most analysis of Cosmic Microwave Background spherical harmonic coefficients a_lm has focused on estimating the power spectrum C_l=<|a_lm|^2> rather than the coefficients themselves. We present a minimum-variance method for measuring a_lm…

We introduce LOT Wassmap, a computationally feasible algorithm to uncover low-dimensional structures in the Wasserstein space. The algorithm is motivated by the observation that many datasets are naturally interpreted as probability…

We consider the problem of finding a basis of a matroid with weight exactly equal to a given target. Here weights can be discrete values from $\{-\Delta,\ldots,\Delta\}$ or more generally $m$-dimensional vectors of such discrete values. We…

We study parameterized versions of classical algorithms for computing shortest-path trees. This is most easily expressed in terms of tropical geometry. Applications include shortest paths in traffic networks with variable link travel times.

Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a…

Sub-pixel matching of multimodal optical images is a critical step in combined application of multiple sensors. However structural noise and inconsistencies arising from variations in multimodal image responses usually limit the accuracy of…

Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference…