Courses/Distributed Systems

Distributed Systems

CS3.401

Prof. Kishore Kothapalli•Monsoon 2025-26•4 credits

Revision Notes/Unit 10 — Distributed Minimum Spanning Tree (GHS Algorithm)

Unit 10 — Distributed Minimum Spanning Tree (GHS Algorithm)

Gallager-Humblet-Spira (1983): the canonical distributed MST algorithm. Cycle and cut properties. Fragments (subtrees of MST) with (name, level). Combining rules A (absorption), B (merger), C (wait). Test/Accept/Reject mechanism on basic edges. Max level ≤ log N. Complexity O(N log N + E) messages — optimal among comparison-based.

GHS Rules A/B/C + Fragment Levels + Test/Accept/Reject

16 min

Computing a minimum spanning tree centrally is easy (Prim, Kruskal). Doing it without a central coordinator — each node only knows its incident edges and their weights — is harder. GHS is **distributed Kruskal**: many small fragments grow in parallel, repeatedly absorbing or merging via their minimum outgoing edge (MWOE). Three combining rules manage the growth: smaller fragments rush into larger ones immediately (A); equal-level fragments merge only if they both chose the same edge (B); otherwise wait (C).