A Ranking Framework for Network Resource Allocation and Scheduling via Hypergraphs (2506.01571v1)

Abstract: Resource allocation and scheduling are a common problem in various distributed systems. Although widely studied, the state-of-the-art solutions either do not scale or lack the expressive power to capture the most complex instances of the problem. To that end, we present a mathematical framework for hypergraph ranking and analysis, unifying graph theory, lattice theory, and semantic analysis. In our fundamental theorem, we prove the existence of partial order on entities of hypergraphs, extending traditional hypergraph analysis by introducing semantic operators that capture relationships between vertices and hyperedges. Within the boundaries of our framework, we introduce an algorithm to rank the node-hyperedge pairs with respect to the captured semantics. The strength of our approach lies in its applicability to complex ranking problems that can be modeled as hypergraphs, including network resource allocation, task scheduling, and table selection in Text-to-SQL. Through simulations, we demonstrate that our framework delivers nearly optimal problem solutions at a superior run time performance.