Related papers: An exact algorithm with the time complexity of $O^…
We present an exact algorithm that decides, for every fixed $r \geq 2$ in time $O(m) + 2^{O(k^2)}$ whether a given multiset of $m$ clauses of size $r$ admits a truth assignment that satisfies at least $((2^r-1)m+k)/2^r$ clauses. Thus…
We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create an…
We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…
Deep learning-based computer-aided diagnosis has achieved unprecedented performance in breast cancer detection. However, most approaches are computationally intensive, which impedes their broader dissemination in real-world applications. In…
We investigate the parameterized complexity of Vertex Cover parameterized by the difference between the size of the optimal solution and the value of the linear programming (LP) relaxation of the problem. By carefully analyzing the change…
We investigate computational problems involving large weights through the lens of kernelization, which is a framework of polynomial-time preprocessing aimed at compressing the instance size. Our main focus is the weighted Clique problem,…
The maximum independent set problem is a classic optimization problem that has also been studied quite intensively in the distributed setting. While the problem is hard to approximate in general, there are good approximation algorithms…
This study considers the (soft) capacitated vertex cover problem in a dynamic setting. This problem generalizes the dynamic model of the vertex cover problem, which has been intensively studied in recent years. Given a dynamically changing…
A set of points and a positive integer $m$ are given and our goal is to cover the maximum number of these point with $m$ disks. We devise the first output sensitive algorithm for this problem. We introduce a parameter $\rho$ as the maximum…
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 present an algorithm for the extensively studied Long Path and Long Cycle problems on unit disk graphs that runs in time $2^{O(\sqrt{k})}(n+m)$. Under the Exponential Time Hypothesis, Long Path and Long Cycle on unit disk graphs cannot…
Finding a low-weight multiple (LWPM) of a given polynomial is very useful in the cryptanalysis of stream ciphers and arithmetic in finite fields. There is no known deterministic polynomial time complexity algorithm for solving this problem,…
Consider a scheduling problem in which jobs need to be processed on a single machine. Each job has a weight and is composed of several operations belonging to different families. The machine needs to perform a setup between the processing…
In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and…
We propose an exact polynomial algorithm for a resource allocation problem with convex costs and constraints on partial sums of resource consumptions, in the presence of either continuous or integer variables. No assumption of strict…
Maximal Independent Set selection is a fundamental problem in distributed computing. A novel probabilistic algorithm for this problem has recently been proposed by Afek et al, inspired by the study of the way that developing cells in the…
We resolve the space complexity of single-pass streaming algorithms for approximating the classic set cover problem. For finding an $\alpha$-approximate set cover (for any $\alpha= o(\sqrt{n})$) using a single-pass streaming algorithm, we…
In this work, we study and analyze different feature selection algorithms that can be used to classify cancer subtypes in case of highly varying high-dimensional data. We apply three different feature selection methods on five different…
In a classical scheduling problem, we are given a set of $n$ jobs of unit length along with precedence constraints, and the goal is to find a schedule of these jobs on $m$ identical machines that minimizes the makespan. Using the standard…
This paper gives poly-logarithmic-round, distributed D-approximation algorithms for covering problems with submodular cost and monotone covering constraints (Submodular-cost Covering). The approximation ratio D is the maximum number of…