Distributed Computing Through Combinatorial Topology Pdf Jun 2026

If the algorithm requires solving consensus ($k=1$), the output shape is a set of disconnected points. However, the input shape is connected. A continuous map cannot take a connected shape and map it to a disconnected shape without tearing it.

Indistinguishability — when two global configurations look identical to a given process — partitions vertices into equivalence classes that naturally form simplicial structures. These structures make it possible to apply algebraic-topological invariants to distributed tasks. distributed computing through combinatorial topology pdf