DB(α) Bipartite Matching

Interactive visualization of the single-round matching protocol from arXiv:2604.10744 (“Bipartite matching under communication constraints”).

Protocol parameters

Nodes / side (N)14

Traffic model (arrivals)

Arrival rate λ
per pair · per round0.030

Size distribution

Mean size (× BDP)

Messages arrive at each sender–receiver pair as a Poisson process of rate λ. Sizes are in multiples of the bandwidth-delay product (BDP). Short messages ≤ 1 BDP bypass matching (served immediately); long messages queue at senders and are matched one per pair per round.

GRANT rule — degree bias

Exponent α0.00

Greedy (α = −∞)

Sender picks receiver v with prob ∝ deg(v)^α. α=0: uniform · α<0: favors low-degree receivers · −∞: pick a minimum-degree neighbor.

Thinning (NOTIFY subsampling)

Mode

Each sender keeps only a random subset of its feasible edges before NOTIFY. max(k=2) + greedy = the paper’s tuning-free 2CGS algorithm.

Playback

Speed1.0×

Show feasible edges

Round statistics

Matched this round	—
Max matching (oracle)	—
Grant collisions	—
Queued (long msgs)	—
Cumulative served	—
Short msgs served	—
Offered load ρ	—
Control messages / round	—
Edges feasible → intent	—
Effective α / thinning	— · —

Effect of α (Monte Carlo)

Sweep graph settings (synthetic D-out random graphs, N=144)

MC mean degree 𝔼D4

MC degree law D

The live simulation's feasible graph emerges from arrivals; these settings only affect the Monte-Carlo sweep above (mean matched fraction vs α over 120 random graphs, no thinning vs current thinning; dotted marker = current α).

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