REST: Receding Horizon Explorative Steiner Tree for Zero-Shot Object-Goal Navigation

Zero-shot object-goal navigation (ZSON) requires navigating unknown environments to find a target object without task-specific training. Prior hierarchical training-free solutions invest in scene understanding (\textit{belief}) and high-level decision-making (\textit{policy}), yet overlook the design of \textit{option}, i.e., a subgoal candidate proposed from evolving belief and presented to policy for selection. In practice, options are reduced to isolated waypoints scored independently: single destinations hide the value gathered along the journey; an unstructured collection obscures the relationships among candidates. Our insight is that the option space should be a \textit{tree of paths}. Full paths expose en-route information gain that destination-only scoring systematically neglects; a tree of shared segments enables coarse-to-fine LLM reasoning that dismisses or pursues entire branches before examining individual leaves, compressing the combinatorial path space into an efficient hierarchy. We instantiate this insight in \textbf{REST} (Receding Horizon Explorative Steiner Tree), a training-free framework that (1) builds an explicit open-vocabulary 3D map from online RGB-D streams; (2) grows an agent-centric tree of safe and informative paths as the option space via sampling-based planning; and (3) textualizes each branch into a spatial narrative and selects the next-best path through chain-of-thought LLM reasoning. Across the Gibson, HM3D, and HSSD benchmarks, REST consistently ranks among the top methods in success rate while achieving the best or second-best path efficiency, demonstrating a favorable efficiency-success balance.