Topological superconductors have shown great potential in the search for unique quasiparticles such as Majorana fermions. Combining nontrivial band topology and superconductivity can lead to topological superconductivity due to the proximity effect. In this work, we used first principle calculations to predict that rock-salt phases of VC and CrC are superconducting with topologically nontrivial states. The phonon dispersions of these transition metal carbides displayed no imaginary frequencies, which suggests dynamic stability. Additionally, the presence of soft acoustic phonon bands supports the existence of Bardeen-Cooper-Schrieffer (BCS) superconductivity in rock-salt VC and CrC. Therefore, these transition metal carbides are practical candidates for studying topological superconductors and their associated Majorana bound states.

This work addresses a Multi-Objective Shortest Path Problem (MO-SPP) on a graph where the goal is to find a set of Pareto-optimal solutions from a start node to a destination in the graph. A family of approaches based on MOA* have been developed to solve MO-SPP in the literature. Typically, these approaches maintain a "frontier" set at each node during the search process to keep track of the non-dominated, partial paths to reach that node. This search process becomes computationally expensive when the number of objectives increases as the number of Pareto-optimal solutions becomes large. In this work, we introduce a new method to efficiently maintain these frontiers for multiple objectives by incrementally constructing balanced binary search trees within the MOA* search framework. We first show that our approach correctly finds the Pareto-optimal front, and then provide extensive simulation results for problems with three, four and five objectives to show that our method runs faster than existing techniques by up to an order of magnitude.

This work addresses the Multi-Objective Shortest Path Problem (MO-SPP): Given a graph where each edge is associated with a non-negative cost vector, MO-SPP aims to find all the Pareto-optimal paths connecting the given start and goal nodes. To solve MO-SPP, the popular multi-objective A* (MOA*) like algorithms maintain a "frontier" set at any node during the search to keep track of the non-dominated paths that reach that node. The computational efficiency of MOA* algorithms directly depend on how efficiently one can maintain the frontier sets. Recently, several techniques have been developed in the literature to address this issue mainly for two objectives. In this work, we introduce a new method to efficiently maintain these frontiers for multiple objectives by leveraging balanced binary search trees. We provide extensive simulation results for problems with three, four and five objectives to show that our method outperforms existing techniques by an order of magnitude in general.