Analyze the time and space complexity of your solution. Compare your solution to others and identify areas for improvement. Refactor your code for readability and maintainability. Document your code ...

Abstract: In undirected graphs with real non-negative weights, we give a new randomized algorithm for the single-source shortest path (SSSP) problem with running time ...

Abstract: We present a study of multithreaded implementations of Thorup's algorithm for solving the Single Source Shortest Path (SSSP) problemfor undirected graphs. Our implementations leverage ...

the objective value of the each Pareto-optimal label path_list List, the path of each Pareto-optimal label queue The priority queue, which outputs the label that has the minimum value of the summation ...

To ensure fine-grained evaluation, we introduce a graph-based CoT consistency metric that verifies whether the reasoning path of model adheres to valid physical logic. Additionally, we minimize ...