Related papers: On Simplifying Dependent Polyhedral Reductions
How data is represented and operationalized is critical for building computational solutions that are both effective and efficient. A common approach is to represent data objects as binary vectors, denoted \textit{hash codes}, which require…
The automaton constrained tree knapsack problem is a variant of the knapsack problem in which the items are associated with the vertices of the tree, and we can select a subset of items that is accepted by a top-down tree automaton. If the…
A product of cochains in a polyhedral complex is constructed. The multiplication algorithm depends on the choice of a parameter. The parameter is a linear functional on the ambient space. Cocycles form a subring of the ring of cochains,…
Semisort is a fundamental algorithmic primitive widely used in the design and analysis of efficient parallel algorithms. It takes input as an array of records and a function extracting a \emph{key} per record, and reorders them so that…
Computing multivariate derivatives of matrix-like expressions in the compact, coordinate free fashion is very important for both theory and applied computations (e.g. optimization and machine learning). The critical components of such…
Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…
Regression problems assume every instance is annotated (labeled) with a real value, a form of annotation we call \emph{strong guidance}. In order for these annotations to be accurate, they must be the result of a precise experiment or…
Compression aims to reduce the size of an input, while maintaining its relevant properties. For multi-parameter persistent homology, compression is a necessary step in any computational pipeline, since standard constructions lead to large…
Given a compact parameter set $Y\subset R^p$, we consider polynomial optimization problems $(P_y$) on $R^n$ whose description depends on the parameter $y\inY$. We assume that one can compute all moments of some probability measure $\phi$ on…
Lokshtanov et al.~[STOC 2017] introduced \emph{lossy kernelization} as a mathematical framework for quantifying the effectiveness of preprocessing algorithms in preserving approximation ratios. \emph{$\alpha$-approximate reduction rules}…
Polynomial multiplication is a fundamental problem in symbolic computation. There are efficient methods for the multiplication of two univariate polynomials. However, there is rarely efficiently nontrivial method for the multiplication of…
The choice of how to represent an abstract type can have a major impact on the performance of a program, yet mainstream compilers cannot perform optimizations at such a high level. When dealing with optimizations of data type…
Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…
Counting distinct permutations with replacement, especially when involving multiple subwords, is a longstanding challenge in combinatorial analysis, with critical applications in cryptography, bioinformatics, and statistical modeling. This…
We focus on modeling the relationship between an input feature vector and the predicted outcome of a trained decision tree using mixed-integer optimization. This can be used in many practical applications where a decision tree or tree…
Semidefinite relaxations are widely used to compute upper bounds on the objective of optimization problems involving noncommutative polynomials. Such optimization problems are prevalent in quantum information. We present an algorithm able…
We consider the class of counting problems,i.e. functions in $\#$P, which are self reducible, and have easy decision version, i.e. for every input it is easy to decide if the value of the function $f(x)$ is zero. For example,…
Pseudoentropy characterizations provide a quantitatively precise demonstration of the close relationship between computational hardness and computational randomness. We prove a unified pseudoentropy characterization that generalizes and…
The synthesis of classical Computational Complexity Theory with Recursive Analysis provides a quantitative foundation to reliable numerics. Here the operators of maximization, integration, and solving ordinary differential equations are…
Circuits play a fundamental role in polyhedral theory and linear programming. For instance, circuits are used as step directions in various augmentation schemes for solving linear programs or to leave degenerate vertices while running the…