arXiv subjects

Randal Tuggle

Publications and source records attributed to Randal Tuggle.

2 recordsLinked to original sources

arXiv2026

NP-Hardness of Non-Crossing Hamiltonian Path and Cycle in Non-Planar Graphs

We seek to disentangle the hardness of finding a Hamiltonian path or cycle from the hardness of finding a non-crossing path or cycle by giving a direct reduction from 3-SAT to the non-crossing Hamiltonian path and cycle problems on non-planar graphs. Prior hardness proofs proceed by reduction to planar graphs, where every path is automatically non-crossing; this conflates the two sources of difficulty and leaves unclear why forbidding crossings on the path alone makes the problem hard. Our reduction places the difficulty squarely in the non-crossing constraint, avoids planar gadget constructions, and yields a more transparent proof that may be easier to extend to related problems.

cs.CG↗

arXiv2020

Accelerating the Distributed Kaczmarz Algorithm by Strong Over-relaxation

The distributed Kaczmarz algorithm is an adaptation of the standard Kaczmarz algorithm to the situation in which data is distributed throughout a network represented by a tree. We isolate substructures of the network and study convergence of the distributed Kazmarz algorithm for relatively large relaxation parameters associated to these substructures. If the system is consistent, then the algorithm converges to the solution of minimal norm; however, if the system is inconsistent, then the algorithm converges to an approximated least-squares solution that is dependent on the parameters and the network topology. We show that the relaxation parameters may be larger than the standard upper-bound in literature in this context and provide numerical experiments to support our results.

math.NA↗