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In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
The P versus NP problem asks whether every language verifiable in polynomial time can also be decided in deterministic polynomial time. In this paper, we present a constructive proof that P = NP by introducing a universal, graph-based…
The personnel rostering problem is the problem of finding an optimal way to assign employees to shifts, subject to a set of hard constraints which all valid solutions must follow, and a set of soft constraints which define the relative…
Moss and Rabani[12] study constrained node-weighted Steiner tree problems with two independent weight values associated with each node, namely, cost and prize (or penalty). They give an O(log n)-approximation algorithm for the…
We study the computational complexity of the non-preemptive scheduling problem of a list of independent jobs on a set of identical parallel processors with a makespan minimization objective. We make a maiden attempt to explore the…
Reconciling a gene tree with a species tree is an important task that reveals much about the evolution of genes, genomes, and species, as well as about the molecular function of genes. A wide array of computational tools have been devised…
We consider the problem of stabilizing an unstable plant driven by bounded noise over a digital noisy communication link, a scenario at the heart of networked control. To stabilize such a plant, one needs real-time encoding and decoding…
A framework consists of an undirected graph $G$ and a matroid $M$ whose elements correspond to the vertices of $G$. Recently, Fomin et al. [SODA 2023] and Eiben et al. [ArXiV 2023] developed parameterized algorithms for computing paths of…
The purpose of this paper is two-fold, first, to review a recent method introduced by S. Becker, P. Cheridito, and P. Jentzen, for solving high-dimensional optimal stopping problems using deep Neural Networks, second, to propose an…
We consider metrical task systems on tree metrics, and present an $O(\mathrm{depth} \times \log n)$-competitive randomized algorithm based on the mirror descent framework introduced in our prior work on the $k$-server problem. For the…
Due to its broad applications in practice, the minimum spanning tree problem and its all kinds of variations have been studied extensively during the last decades, for which a host of efficient exact and heuristic algorithms have been…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
Despite the latest prevailing success of deep neural networks (DNNs), several concerns have been raised against their usage, including the lack of intepretability the gap between DNNs and other well-established machine learning models, and…
We consider the Steiner tree problem on graphs where we are given a set of nodes and the goal is to find a tree sub-graph of minimum weight that contains all nodes in the given set, potentially including additional nodes. This is a…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
Directed Steiner Tree (DST) is a central problem in combinatorial optimization and theoretical computer science: Given a directed graph $G=(V, E)$ with edge costs $c \in \mathbb{R}_{\geq 0}^E$, a root $r \in V$ and $k$ terminals $K\subseteq…
We consider global problems, i.e. problems that take at least diameter time, even when the bandwidth is not restricted. We show that all problems considered admit efficient solutions in low-treewidth graphs. By ``efficient'' we mean that…
Modern manufacturing systems must meet hard delivery deadlines while coping with stochastic task durations caused by process noise, equipment variability, and human intervention. Traditional deterministic schedules break down when reality…
Many existing algorithms for streaming geometric data analysis have been plagued by exponential dependencies in the space complexity, which are undesirable for processing high-dimensional data sets. In particular, once $d\geq\log n$, there…
We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on $n$ vertices and $m$ edges using $\text{polylog}(n)$ calls to any maximum flow subroutine. Using the current best deterministic maximum flow…