Related papers: Product Subset Problem : Applications to number th…
This article details the algorithmics in FLSSS, an R package for solving various subset sum problems. The fundamental algorithm engages the problem via combinatorial space compression adaptive to constraints, relaxations and variations that…
The automaton constrained tree knapsack problem is a variant of the knapsack problem in which the items are associated with the vertices of the tree, and we can select a subset of items that is accepted by a top-down tree automaton. If the…
We consider the algorithmic problem of finding a near-optimal solution for the number partitioning problem (NPP). The NPP appears in many applications, including the design of randomized controlled trials, multiprocessor scheduling, and…
Subset-sum problems belong to the NP class and play an important role in both complexity theory and knapsack-based cryptosystems, which have been proved in the literature to become hardest when the so-called density approaches one. Lattice…
The development of a satisfying and rigorous mathematical understanding of the performance of neural networks is a major challenge in artificial intelligence. Against this background, we study the expressive power of neural networks through…
The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems. The main result is an $\widetilde{O}(n+1/\varepsilon^{5/3})$ time randomized FPTAS for Partition, which is…
The Bin Packing Problem (BPP) stands out as a paradigmatic combinatorial optimization problem in logistics. Quantum and hybrid quantum-classical algorithms are expected to show an advantage over their classical counterparts in obtaining…
We present a quantum probabilistic algorithm which tests with a polynomial computational complexity whether a given composite number is of the Carmichael type. We also suggest a quantum algorithm which could verify a conjecture by…
In the knapsack problems with neighborhood constraints that were studied before, the input is a graph $\mathcal{G}$ on a set $\mathcal{V}$ of items, each item $v \in \mathcal{V}$ has a weight $w_v$ and profit $p_v$, the size $s$ of the…
A multiple knapsack constraint over a set of items is defined by a set of bins of arbitrary capacities, and a weight for each of the items. An assignment for the constraint is an allocation of subsets of items to the bins which adheres to…
The Bin Packing Problem (BPP) is a well-established combinatorial optimization (CO) problem. Since it has many applications in our daily life, e.g. logistics and resource allocation, people are seeking efficient bin packing algorithms. On…
We systematize software side-channel attacks with a focus on vulnerabilities and countermeasures in the cryptographic implementations. Particularly, we survey past research literature to categorize vulnerable implementations, and identify…
Evolutionary algorithms have been applied to a wide range of stochastic problems. Motivated by real-world problems where constraint violations have disruptive effects, this paper considers the chance-constrained knapsack problem (CCKP)…
We consider a variant of the knapsack problem, where items are available with different possible weights. Using a separate budget for these item improvements, the question is: Which items should be improved to which degree such that the…
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding.…
In this paper, we investigate the control of a cyber-physical system (CPS) while accounting for its vulnerability to external attacks. We formulate a constrained stochastic problem with a robust constraint to ensure robust operation against…
Parameterized complexity enables the practical solution of generally intractable NP-hard problems when certain parameters are small, making it particularly useful in real-world applications. The study of string problems in this framework…
In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In…
This thesis centers around the concept of Subset Search Problems (SSP), a type of computational problem introduced by Gr\"une and Wulf to analyze the complexity of more intricate optimization problems. These problems are given an input set,…
Link failures in wide area networks are common and cause significant data losses. Mesh-based protection schemes offer high capacity efficiency but they are slow and require complex signaling. Additionally, real-time reconfiguration of a…