Algorithms, Computational Complexity Theory, Computational Geometry, and Categorical Methods Theory with Applications

Dear Colleagues,

Algorithms, computational complexity theory, computational geometry, and categorical methods form a core toolkit for understanding efficiency, structure, and compositionality in modern computation. In an era of unprecedented computational power and data proliferation—where software permeates science and industry—the efficiency, correctness, and scalability of systems are more critical than ever. We face the following pressing questions: Which problems admit efficient algorithms? What lower bounds delineate intrinsic hardness? How can geometric structure be exploited in data analysis and optimization? And how can categorical abstractions unify models, proofs, and implementations across domains?

This Special Issue will bring together these synergistic pillars of theoretical computer science to explore the interplay between classical foundations and contemporary applications. Our aim is to illuminate new research directions and foster a deeper, structural understanding of computation, from rigorous theory to real-world impact.

We welcome state-of-the-art contributions across the following (non-exhaustive) areas:

• Algorithms and Optimization: Design and analysis; algorithm engineering; approximation and randomized methods; de-randomization; online, parallel, distributed, streaming, sublinear/sketching paradigms; and specialized data structures.
• Computational Complexity: Complexity classes (e.g., P vs. NP and beyond); fine-grained and parameterized complexity; circuit, proof, and communication complexity; hardness of approximation; conditional lower bounds; and quantum/classical comparisons.
• Computational Geometry and Topology: Geometric data structures; convexity and arrangements; hulls, Voronoi diagrams, triangulations; geometric optimization; mesh generation; computational topology and topological data analysis; and applications in graphics, robotics, GIS, CAD, and vision.
• Interdisciplinary Applications: Theory-driven advances in cryptography, bioinformatics, network science, data science, and artificial intelligence.

Submissions will be accepted on a rolling basis until the deadline. All manuscripts will undergo rigorous peer review, and acceptance will be based on quality, originality, and relevance to this Special Issue.

Dr. Yiyang Jia
Dr. Emil Saucan
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.