This paper presents an O(1.2738 + kn)-time polynomial-space algorithm for VERTEX COVER improving both the previous O(1.286 +kn)-time polynomial-space algorithm by Chen, Kanj, and Jia, and the very recent O(1.2745k + kn)time exponential-space algorithm, by Chandran and Grandoni. Most of the previous algorithms rely on exhaustive case-bycase analysis, and an underlying conservative worst-case-sce...

The multiple UnderWater Sink (UW-Sink) architecture is introduced to resolve the scalability problem in USNs. To maximize the benefit of this architecture, the UW-Sinks should be located carefully. Previously, we proposed Minimum d-Hop UW-Sink Placement Problem (MdHUWSPP) for time-sensitive applications, whose objective is minimizing the number of UW-Sinks which d-hop dominate a given USN. In t...

Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the Hamiltonian system is refactorized using polynomial symplectic maps. This method is analyzed in detail for the three degree of freedom case. We obtain explicit ...

We develop a new constraint-reduced infeasible predictor-corrector interior point method for semidefinite programming, and we prove that it has polynomial global convergence and superlinear local convergence. While the new algorithm uses HKM direction in predictor step, it adopts AHO direction in corrector step to achieve a faster approach to the central path. In contrast to the previous constr...