Polynomial-Time Analytical Relaxation of the Travelling Salesman Problem via Probability-Flow Tensors and Maclaurin Series Expansions
Year: 2026
Type: article
Abstract: The Travelling Salesman Problem (TSP) remains a canonical NP-hard combinatorial optimization challenge,traditionally bound by factorial O(N!) or exponential O(N² 2^N) computational complexities. This paperpresents a novel continuous-analytical framework that maps discrete permutation spaces onto a continuousprobability-flow tensor manifold. By reformulating edge transitions through stochastic matrices, cumulativeproduct normalization, transcendental scaling factors, and truncated Maclaurin series expansions of pathgenerating functions, we bypass exponential subset enumeration. We introduce a deterministic algorithmexecuting in strict O(N³) polynomial time, demonstrating empirical alignment with known optimal baselineswhile ensuring stable scalability for enterprise-scale graph topologies.
Author: Udaysagar Kandpal
Institution: Jaypee Institute of Information Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7225383010