Efficient planning and sequence selection are central to intelligence, yet current approaches remain largely incompatible with biological computation. Classical graph algorithms like Dijkstra's or A* require global state and biologically implausible operations such as backtracing, while reinforcement learning methods rely on slow gradient-based policy updates that appear inconsistent with rapid behavioral adaptation observed in natural systems. We propose a biologically plausible algorithm for shortest-path computation that operates through local spike-based message-passing with realistic processing delays. The algorithm exploits spike-timing coincidences to identify nodes on optimal paths: Neurons that receive inhibitory-excitatory message pairs earlier than predicted reduce their response delays, creating a temporal compression that propagates backwards from target to source. Through analytical proof and simulations on random spatial networks, we demonstrate that the algorithm converges and discovers all shortest paths using purely timing-based mechanisms. By showing how short-term timing dynamics alone can compute shortest paths, this work provides new insights into how biological networks might solve complex computational problems through purely local computation and relative spike-time prediction. These findings open new directions for understanding distributed computation in biological and artificial systems, with possible implications for computational neuroscience, AI, reinforcement learning, and neuromorphic systems.