arXiv subjects
Publications and source records attributed to Scott Wynn.
We compute the truncated point schemes of subalgebras of Fomin-Kirillov algebras associated with certain graphs. While Fomin-Kirillov algebras do not admit any truncated point modules, we prove a tight bound on the degrees of truncated point modules over generalized Fomin-Kirillov algebras associated with trees.
Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable matching algorithm using $n^2$ processors that converges in $O(n log(n))$ average runtime. The algorithm is structurally based on the Parallel Iterative Improvement (PII) algorithm, where we improve the convergence rate from $90\%$ to $100\%$ over a large number of trials. We suggest alternative selection methods for pairs in the PII algorithm, called Right-Minimum and Dynamic Selection, as well as a faster preprocessing step, called Quick Initialization, resulting in full convergence over $3.6$ million trials and significantly improved runtime.