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We introduce the \emph{submodular objectives chasing problem}, which generalizes many natural and previously-studied problems: a sequence of constrained submodular maximization problems is revealed over time, with both the objective and…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
In the classic Integer Programming (IP) problem, the objective is to decide whether, for a given $m \times n$ matrix $A$ and an $m$-vector $b=(b_1,\dots, b_m)$, there is a non-negative integer $n$-vector $x$ such that $Ax=b$. Solving (IP)…
We present novel homomorphic encryption schemes for integer arithmetic, intended for use in secure single-party computation in the cloud. These schemes are capable of securely computing only low degree polynomials homomorphically, but this…
The graph isomorphism problem is theoretically interesting and also has many practical applications. The best known classical algorithms for graph isomorphism all run in time super-polynomial in the size of the graph in the worst case. An…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
Graph pattern matching is a routine process for a wide variety of applications such as social network analysis. It is typically defined in terms of subgraph isomorphism which is NP-Complete. To lower its complexity, many extensions of graph…
The monotone minimal perfect hash function (MMPHF) problem is the following indexing problem. Given a set $S= \{s_1,\ldots,s_n\}$ of $n$ distinct keys from a universe $U$ of size $u$, create a data structure $DS$ that answers the following…
We investigate the complexity of isomorphism relations for classes of finitely generated and n-generated computably enumerable (c.e.) algebras, presented via c.e. presentations -- that is, as quotients of term algebras over decidable sets…
This work studies fundamental limits for recovering the underlying correspondence among multiple correlated graphs. In the setting of inhomogeneous random graphs, we present and analyze a matching algorithm: first partially match the graphs…
We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the…
The group isomorphism problem asks whether two finite groups given by their Cayley tables are isomorphic or not. Although there are polynomial-time algorithms for some specific group classes, the best known algorithm for testing isomorphism…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
Graph Isomorphism is the prime example of a computational problem with a wide difference between the best known lower and upper bounds on its complexity. We bridge this gap for a natural and important special case, planar graph isomorphism,…
In recent years, we have seen several approaches to the graph isomorphism problem based on "generic" mathematical programming or algebraic (Gr\"obner basis) techniques. For most of these, lower bounds have been established. In fact, it has…
Near isometric orthogonal embeddings to lower dimensions are a fundamental tool in data science and machine learning. In this paper, we present the construction of such embeddings that minimizes the maximum distortion for a given set of…
A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…
The Tensor Isomorphism problem (TI) has recently emerged as having connections to multiple areas of research within complexity and beyond, but the current best upper bound is essentially the brute force algorithm. Being an algebraic…
In this paper, we propose a high-order extension of the multiscale method introduced by the authors in [SIAM J. Numer. Anal., 63(4) (2025), pp. 1617--1641] for heterogeneous Stokes problems, while also providing several other improvements,…
In this paper we propose an algorithm for exact partitioning of high-order models. We define a general class of $m$-degree Homogeneous Polynomial Models, which subsumes several examples motivated from prior literature. Exact partitioning…