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Recently there has been a lot of progress in the development of economic nonlinear model predictive control (NMPC) schemes for multistage optimal power flow (OPF) problems. However, the additional inclusion of discrete decision variables to…
We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value…
The Maximum Betweenness Centrality problem (MBC) can be defined as follows. Given a graph find a $k$-element node set $C$ that maximizes the probability of detecting communication between a pair of nodes $s$ and $t$ chosen uniformly at…
Quantum Parametric Circuits are constructed as an alternative to reduce the size of quantum circuits, meaning to decrease the number of quantum gates and, consequently, the depth of these circuits. However, determining the optimal circuit…
The global scarcity of GPUs necessitates more sophisticated strategies for Deep Learning jobs in shared cluster environments. Accurate estimation of how much GPU memory a job will require is fundamental to enabling advanced scheduling and…
Circuit augmentation schemes are a family of combinatorial algorithms for linear programming that generalize the simplex method. To solve the linear program, they construct a so-called monotone circuit walk: They start at an initial vertex…
What is the power of constant-depth circuits with $MOD_m$ gates, that can count modulo $m$? Can they efficiently compute MAJORITY and other symmetric functions? When $m$ is a constant prime power, the answer is well understood: Razborov and…
Mobile edge computing (MEC) networks are one of the key technologies for ultra-reliability and low-latency communications. The computing resource allocation solution needs to be carefully designed to guarantee the computing resource…
We investigate monotone circuits with local oracles [K., 2016], i.e., circuits containing additional inputs $y_i = y_i(\vec{x})$ that can perform unstructured computations on the input string $\vec{x}$. Let $\mu \in [0,1]$ be the locality…
Maximal Independent Set (MIS) is one of the fundamental problems in distributed computing. The round (time) complexity of distributed MIS has traditionally focused on the \emph{worst-case time} for all nodes to finish. The best-known…
Neural gates compute functions based on weighted sums of the input variables. The expressive power of neural gates (number of distinct functions it can compute) depends on the weight sizes and, in general, large weights (exponential in the…
Despite progress in quantum Hamiltonian complexity, little is known about the computational complexity of quantum physics at the thermodynamic limit. Even defining the problem is not straight forward. We study the complexity of estimating…
Theoretical complexity is a vital subfield of computer science that enables us to mathematically investigate computation and answer many interesting queries about the nature of computational problems. It provides theoretical tools to assess…
Despite major ongoing advancements in neutral atom hardware technology, there remains limited work in systems-level software tailored to overcoming the challenges of neutral atom quantum computers. In particular, most current neutral atom…
LECTURE GIVEN AT TH2002. Given a set of Boolean variables, and some constraints between them, is it possible to find a configuration of the variables which satisfies all constraints? This problem, which is at the heart of combinatorial…
The maximum modularity of a graph is a parameter widely used to describe the level of clustering or community structure in a network. Determining the maximum modularity of a graph is known to be NP-complete in general, and in practice a…
Multiplication is one of the most fundamental computational problems, yet its true complexity remains elusive. The best known upper bound, by F\"{u}rer, shows that two $n$-bit numbers can be multiplied via a boolean circuit of size $O(n \lg…
The Partitioning Min-Max Weighted Matching (PMMWM) problem is an NP-hard problem that combines the problem of partitioning a group of vertices of a bipartite graph into disjoint subsets with limited size and the classical Min-Max Weighted…
Let $P$ be a set of $2n$ points in the plane, and let $M_{\rm C}$ (resp., $M_{\rm NC}$) denote a bottleneck matching (resp., a bottleneck non-crossing matching) of $P$. We study the problem of computing $M_{\rm NC}$. We first prove that the…
In monotone classification, the input is a multi-set $P$ of points in $\mathbb{R}^d$, each associated with a hidden label from $\{-1, 1\}$. The goal is to identify a monotone function $h$, which acts as a classifier, mapping from…