Distributed algorithms for building Hamiltonian cycles in k-ary n-cubes and hypercubes with faulty links (2007)
Journal Article
Stewart, I. (2007). Distributed algorithms for building Hamiltonian cycles in k-ary n-cubes and hypercubes with faulty links. Journal of Interconnection Networks, 8(3), 253-284. https://doi.org/10.1142/s0219265907002016

We derive a sequential algorithm Find-Ham-Cycle with the following property. On input: k and n (specifying the k-ary n-cube Q(n,k); F, a set of at most 2n-2 faulty links; and v, a node of Q(n,k), the algorithm outputs nodes v+ and v- such that if Fin... Read More about Distributed algorithms for building Hamiltonian cycles in k-ary n-cubes and hypercubes with faulty links.

Constraint satisfaction, logic and forbidden patterns (2007)
Journal Article
Madelaine, F., & Stewart, I. (2007). Constraint satisfaction, logic and forbidden patterns. SIAM Journal on Computing, 37(1), 132-163. https://doi.org/10.1137/050634840

In the early nineties, Feder and Vardi attempted to find a large sub-class of NP which exhibits a dichotomy; that is, where every problem in the sub-class is either solvable in polynomial-time or NP-complete. Their studies resulted in a candidate cla... Read More about Constraint satisfaction, logic and forbidden patterns.