Parametric Traversal for Multi-Dimensional Cost-Aware Graph Reasoning

TL;DR

This paper introduces a parametric traversal framework for multi-dimensional, cost-aware graph reasoning that models both existing and potential infrastructure links, enabling more realistic and flexible network planning.

Contribution

It generalizes classical path search by incorporating gap transitions and multi-dimensional criteria, scalable to large graphs, and applicable to real-world infrastructure design scenarios.

Findings

Demonstrates feasibility of multi-dimensional traversal in datacenter design.

Shows ability to handle non-scalar trade-offs in network routing.

Enables policy calibration beyond classical path search methods.

Abstract

Classical path search assumes complete graphs and scalar optimization metrics, yet real infrastructure networks are incomplete and require multi-dimensional evaluation. We introduce the concept of traversal: a generalization of paths that combines existing edges with gap transitions, missing but acceptable connections representing links that can be built. This abstraction captures how engineers actually reason about infrastructure: not just what exists, but what can be realized. We present a parametric framework that treats planned connections as first-class transitions, scales to large graphs through efficient candidate filtering, and uses multi-dimensional criteria to decide whether a traversal should continue to be explored or be abandoned. We evaluate the framework through representative scenarios in datacenter circuit design and optical route construction in telecommunication networks, demonstrating conditional feasibility, non-scalarizable trade-offs, and policy calibration capabilities beyond the reach of classical formulations.