feat(monitor): communication-efficient distributed L2/F2 monitoring (Count-Sketch + geometric safe-zone) - #378
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Real distributed second-frequency-moment monitor — the L2 counterpart to the L1
slack-countdown coordinator. The hard part is that F2 does NOT merge linearly:
F2(Σ f_i) = Σ F2(f_i) + 2 Σ_{i<j} ⟨f_i, f_j⟩ (cross terms)
so summing per-edge F2 is wrong. Fix (AMS / Cormode–Garofalakis): keep a LINEAR
AMS tug-of-war sketch Z = Σ g(x)f(x) (±1 hash) per edge — Z is linear in updates,
so Z_merged = Σ Z_i and E[Z_merged²] = F2(Σ f_i); squaring the MERGED sketch
recovers the cross terms automatically.
data_plane/src/monitor/f2.rs:
- AmsF2Sketch: update / linear merge / estimate_f2 (mean-of-Z² per group, median
over s2 groups). s1=O(1/ε²) averaging, s2=O(log 1/δ) median.
- DistributedF2Monitor: per-edge sketches, merge-on-report, global F2̂, fires once
at F2̂ ≥ (1−ε)τ.
- sampling_var_budget() = ε²·F2 — the L2 variance budget (ε·‖f‖₂)² for the SAME
per-key p_i ∝ √(f_i/rate_i) allocation (sampling_alloc unchanged; only the
norm in the budget differs from L1's (ε·τ)²).
5 unit tests incl. merge_captures_cross_terms (merged F2̂≈600 not 400) — proving
the non-linear merge is handled. Pure, no I/O.
Scope: this is the data-plane algorithmic core (the novel/hard part), fully
tested. End-to-end transport — extending MonitorReport to carry the AMS sketch,
the edge (Go) computing it, server.rs routing F2 monitors, and the control-plane
emitting a `functional: f2` — is the integration follow-up.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Switch the distributed-F2 estimator from AMS tug-of-war to a Count-Sketch (d rows × w buckets, ±1 sign), matching ASAP's warm-tier sketch family and the UnivMon/Cormode-Garofalakis line. Same linear-merge-captures-cross-terms property (C_merged = Σ C_i, F2̂ = median_r Σ_b C[r][b]²). Hashing = murmur3 fmix64 with a different seed per row and a different salt for bucket vs sign (engineering approximation, like xxhash/murmur — not provably 4-wise independent). DistributedF2Monitor now also does the L2 coordinated-sampling allocation: allocate_p() with freq_i = each edge's LOCAL F2̂_i (from its own sketch), rate_i = reported rate, var_budget = ε²·F2̂_global — so p_i ∝ √(F2̂_i/rate_i) (an edge carrying more L2 mass keeps a higher p). Mirrors the L1 coordinator::allocate_p with the L2 freq/budget. Division of labour: EDGE maintains its local Count-Sketch (shared seeds) + rate and ships (sketch, rate) per window; COORDINATOR merges linearly, estimates F2̂, fires at (1−ε)τ, and allocates p_i. 6 unit tests incl. cross-term merge and equal-rate-different-F2 allocation. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
…CDM-F2) Adds GeometricF2Monitor — the Sharfman–Schuster–Keren safe-zone layer that makes distributed F2 monitoring communication-efficient and BREAKS the circularity "need L2 to decide whether to send, but need the sketch to get L2": each site runs a PURELY LOCAL test — does its drift ball stay inside the safe ball B(0, √(d·τ))? — using only the last-broadcast reference C_ref and its OWN drift ΔC_i, never the live global. A site ships its sketch ONLY when locally unsafe, triggering a resync. Monitored quantity ‖C‖₂² (E=d·F2) vs d·τ; convexity theorem: global C=(1/k)Σu_i is in the convex hull of u_i=C_ref+k·ΔC_i, so all per-site bounding balls ⊆ B(0,R) ⇒ ‖C‖<R ⇒ F2<τ (no missed crossing). F2 is the clean case — its sublevel set is already a ball (no covering spheres). CountSketchF2 gains l2_norm_sq / minus / norm_sq_combo for the ball test. 4 new tests: silent under small drift, trips on threatening drift, stays-silent-then- resyncs (communication savings), alert on resync over τ. 10/10 f2 tests green. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
zzylol
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This was referenced Jun 17, 2026
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The L2 counterpart to the L1 slack-countdown coordinator — real implementation, in two layers.
Layer 1 — correct distributed F2 over Count-Sketches
F2 = ‖f‖₂²does not merge linearly:F2(Σ_i f_i) = Σ_i F2(f_i) + 2 Σ_{i<j} ⟨f_i, f_j⟩. The fix is a linear sketch: a Count-Sketch rowC[r][b] = Σ_{x:h_r(x)=b} s_r(x) f(x)is linear in updates, soC_merged = Σ_i C_iandΣ_b C_merged[r][b]²estimatesF2(Σ_i f_i)— squaring the merged sketch recovers the cross terms.CountSketchF2—drows ×wbuckets, ±1 sign;update/ linearmerge/estimate_f2(median over rows ofΣ_b C[r][b]²);w=O(1/ε²),d=O(log 1/δ). Hashing = murmur3fmix64, different seed per row + different salt for bucket vs sign.DistributedF2Monitor— merges per-edge sketches, estimates globalF2̂, fires atF2̂ ≥ (1−ε)τ, and does the L2 coordinated-sampling allocationp_i ∝ √(F2̂_i / rate_i)(var_budget = ε²·F2̂).Layer 2 — geometric safe-zone (communication-efficient, breaks the circularity)
Shipping the sketch every window defeats CDM and creates a circularity: you need the global L2 to decide whether to send, but you need the sketch to get the L2.
GeometricF2Monitor(Sharfman–Schuster–Keren) resolves it:B(C_ref + (k/2)ΔC_i, (k/2)‖ΔC_i‖)stay inside the safe ballB(0, √(d·τ))? — using only the last-broadcastC_refand its own drift, never the live global.C=(1/k)Σ u_i(u_i=C_ref+k·ΔC_i) is in the convex hull, so all balls ⊆B(0,R)⇒‖C‖<R ⇒ F2<τ(no missed crossing). F2 is the clean case — its sublevel set is already a ball.Tests (10/10)
merge_captures_cross_terms(merged ≈600 not 400),count_sketch_estimates_f2,monitor_alert_threshold,allocate_p_higher_local_f2,sampling_var_budget, and geometric:silent_under_small_drift,triggers_when_drift_threatens_tau,stays_silent_then_resyncs(savings),alert_on_resync_over_tau.Theory anchors
Cormode, "The continuous distributed monitoring model" (SIGMOD Record 2013); Sharfman–Schuster–Keren geometric monitoring; Cormode–Muthukrishnan–Yi distributed functional monitoring. Pairs with L1 per-key-freq allocation (#377).
Scope
Algorithmic core, pure + tested. Transport wiring (sketch in
MonitorReport,C_refbroadcast, edge-side local safe-zone test,server.rsroutingf2, control-planefunctional: f2) is the integration follow-up.🤖 Generated with Claude Code