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This paper studies a scheduling problem in a parallel machine setting, where each machine must adhere to a predetermined fixed order for processing the jobs. Given $n$ jobs, each with processing times and deadlines, we aim to minimize the…
Independent set is a fundamental problem in combinatorial optimization. While in general graphs the problem is essentially inapproximable, for many important graph classes there are approximation algorithms known in the offline setting.…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
In the moldable job scheduling problem one has to assign a set of $n$ jobs to $m$ machines, in order to minimize the time it takes to process all jobs. Each job is moldable, so it can be assigned not only to one but any number of the equal…
We study the problem of clustering networks whose nodes have imputed or physical positions in a single dimension, for example prestige hierarchies or the similarity dimension of hyperbolic embeddings. Existing algorithms, such as the…
In this paper, an operating system scheduling algorithm based on Double DQN (Double Deep Q network) is proposed, and its performance under different task types and system loads is verified by experiments. Compared with the traditional…
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge…
We consider the problem of scheduling $n$ precedence-constrained jobs on $m$ uniformly-related machines in the presence of an arbitrary, fixed communication delay $\rho$. We consider a model that allows job duplication, i.e. processing of…
In this paper we consider several constrained activity scheduling problems in the time and space domains, like finding activity orderings which optimize the values of several objective functions (time scheduling) or finding optimal…
We study a variant of the classical membership problem in automata theory, which consists of deciding whether a given input word is accepted by a given automaton. We do so under a different perspective, that is, we consider a dynamic…
Many signal processing problems can be solved by maximizing the fitness of a segmented model over all possible partitions of the data interval. This letter describes a simple but powerful algorithm that searches the exponentially large…
This paper presents a novel idea for the general case of the Common Due-Date (CDD) scheduling problem. The problem is about scheduling a certain number of jobs on a single or parallel machines where all the jobs possess different processing…
We study the point location problem on dynamic planar subdivisions that allows insertions and deletions of edges. In our problem, the underlying graph of a subdivision is not necessarily connected. We present a data structure of linear size…
Allen's interval algebra is one of the most well-known calculi in qualitative temporal reasoning with numerous applications in artificial intelligence. Recently, there has been a surge of improvements in the fine-grained complexity of…
We study the complexity of a fundamental algorithm for fairly allocating indivisible items, the round-robin algorithm. For $n$ agents and $m$ items, we show that the algorithm can be implemented in time $O(nm\log(m/n))$ in the worst case.…
We develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an $O(f^2)$-approximately optimal solution in $O(f \cdot \log…
In this paper, we consider the problems for covering multiple intervals on a line. Given a set $B$ of $m$ line segments (called "barriers") on a horizontal line $L$ and another set $S$ of $n$ horizontal line segments of the same length in…
Learned indexes leverage machine learning models to accelerate query answering in databases, showing impressive practical performance. However, theoretical understanding of these methods remains incomplete. Existing research suggests that…
We give fast, simple, and implementable catalytic logspace algorithms for two fundamental graph problems. First, a randomized catalytic algorithm for $s\to t$ connectivity running in $\widetilde{O}(nm)$ time, and a deterministic catalytic…
A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that…