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A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
The subset sum problem over finite fields is a well-known {\bf NP}-complete problem. It arises naturally from decoding generalized Reed-Solomon codes. In this paper, we study the number of solutions of the subset sum problem from a…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
Finding two disjoint simple paths on two given sets of points is a geometric problem introduced by Jeff Erickson. This problem has various applications in computational geometry, like robot motion planning, generating polygon etc. We will…
We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop…
Computational complexity of the design problem for a network with a target value of Region-Based Component Decomposition Number (RBCDN) has been proven to be NP-complete.
The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…
Within recent years, considerable progress has been made regarding high-performance solvers for Partial Differential Equations (PDEs), yielding potential gains in efficiency compared to industry standard tools. However, the latter largely…
Emerging analog computing substrates, such as oscillator-based Ising machines, offer rapid convergence times for combinatorial optimization but often suffer from limited scalability due to physical implementation constraints. To tackle…
We consider a class of resource allocation problems given a set of unconditional constraints whose objective function satisfies Bellman's optimality principle. Such problems are ubiquitous in wireless communication, signal processing, and…
The concept of decomposition in computer science and engineering is considered a fundamental component of computational thinking and is prevalent in design of algorithms, software construction, hardware design, and more. We propose a simple…
We study several variations of line segment covering problem with axis-parallel unit squares in $I\!\!R^2$. A set $S$ of $n$ line segments is given. The objective is to find the minimum number of axis-parallel unit squares which cover at…
We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…
We consider a type of optimal switching problems with non-uniform execution delays and ramping. Such problems frequently occur in the operation of economical and engineering systems. We first provide a solution to the problem by applying a…
The question of whether all problems in NP class are also in P class is generally considered one of the most important open questions in mathematics and theoretical computer science as it has far-reaching consequences to other problems in…
This paper addresses the qualitative theory of mixed-order positive linear coupled systems with bounded or unbounded delays. First, we introduce a general result on the existence and uniqueness of solutions to mixed-order linear coupled…
Recent advances in quantum technology have led to the development and manufacturing of experimental programmable quantum annealers that promise to solve certain combinatorial optimization problems of practical relevance faster than their…
A quantum computing scheme that uses a single photon and multiple-slit gratings is suggested for the Hamiltonian path problem on a simple graph G of N vertices. The photon is input to an N-slit grating followed by an N x N matrix of…
The Hamiltonian cycle problem (HCP), which is an NP-complete problem, consists of having a graph G with n nodes and m edges and finding the path that connects each node exactly once. In this paper we compare some algorithms to solve a…
The NP-hard problem of decoding random linear codes is crucial to both coding theory and cryptography. In particular, this problem underpins the security of many code based post-quantum cryptographic schemes. The state-of-art algorithms for…