Discounted Cost Register Automata (DCRA) associate costs with strings in a regular manner using the operation of discounted sum. The min-cost optimization problem for DCRAs corresponds to computing shortest paths in graphs with more general forms of discounting than the well-studied notion of future discounting. We present solutions to two classes of such shortest path problems: in presence of ...

Simple heuristics often show a remarkable performance in practice for optimization problems. Worst-case analysis falls short of explaining this performance. Because this, “beyond worst-case analysis” algorithms has recently gained lot attention, including probabilistic algorithms. The instances many problems are essentially discrete metric space. Probabilistic such nevertheless mostly been cond...

The Shortest Path Problem with Resource Constraints is a common subproblem in many Branch-Cut-and-Price algorithms (BCP), e.g., routing and scheduling problems. This paper presents a general label-setting algorithm for solving various shortest path problems. An integration of the ‘Shortest Path Problem with Resource Constraints and k-cycle elimination’ with the ‘Partial Elementarity’ is introdu...