Formal algorithmic construction of sparse Octopus topologies

Develop formal algorithmic construction methods for sparse Octopus CXL pod topologies, defined as host–multi-headed device bipartite graphs where each host connects to X multi-headed CXL memory devices (MHDs) and pairs of hosts may be arbitrarily far apart (i.e., the topology is not necessarily a balanced incomplete block design). The goal is to systematically generate such sparse Octopus topologies for given parameters (host port count X and MHD port count N) so they can be instantiated and used in practical CXL memory pooling pods.

Background

Octopus is a class of CXL memory pooling pod topologies that connect hosts directly to multi-headed CXL devices (MHDs) without switches. Regular and dense Octopus topologies can be described using balanced incomplete block designs (BIBDs), enabling precise constructions and analysis of pod size and connectivity.

Sparse Octopus topologies relax the BIBD constraints, allowing pairs of hosts to be arbitrarily far apart and enabling specialized structures (e.g., HPC-oriented tori). While the authors outline the promise of sparse designs, they explicitly note that they have not formalized how to algorithmically construct these topologies, leaving a concrete gap between conceptual definitions and practical instantiation.