arXiv subjects

Ian D'Ambrosio

Publications and source records attributed to Ian D'Ambrosio.

4 recordsLinked to original sources

arXiv2026

A Deterministic Constant-Competitive Algorithm for Dynamic Mixture-of-Experts Serving

Dynamic Mixture-of-Experts Serving allocates k replica GPUs among m experts as workloads change. At each round, the online algorithm sees the current workload, chooses integral replica counts, and pays bottleneck service cost plus replica movement. It does not know future workloads. Huang, Lou, and Xiao gave an O(sqrt(log k))-competitive randomized algorithm for this problem. We prove a deterministic O(1)-competitive algorithm. For every number of experts and every k>=1, the algorithm satisfies ALG_det <= 10 C_PB OPT + (5 C_PB + 8) k + 16, where C_PB is the absolute constant from Chasing Positive Bodies at resource augmentation one and covering sparsity two. Consequently, CR_det(k)<=10 C_PB for every k>=1, so CR_det(k)=Theta(1). The multiplicative factor does not depend on the number of experts, replica budget, horizon, or workload values. Thus randomization is not needed for the asymptotic guarantee. The proof has two layers. A finite tangent envelope, summable positive resets, and a nonexpansive balanced projection reduce reciprocal-max service costs to a deterministic exact-budget fractional path. A new deterministic rounding theorem converts every such path to integral allocations with service distortion three and movement bounded by the fractional movement plus 6k. The complete reduction, rounding theorem, causal composition, and quantified main theorem are machine-checked in Lean 4 relative to the positive-body result as the sole scientific source premise. The theorem concerns the allocation model above. It does not include network topology, shared-edge congestion, or routing decisions.

cs.DS↗

arXiv2026

Always-Correct Succinct Dynamic Fusion Nodes Are Impossible: A Cell-Probe Lower Bound in the Small-Set, Large-Universe Regime

Kuszmaul, Liang, and Zhou (SODA 2026) ask whether succinct constant-time dynamic fusion nodes exist when the number of stored keys is polylogarithmic in the universe size. We give a negative answer for always-correct structures. For n^8 <= U, log_2 U >= 2^70, and redundancy 0 <= R < n, a dynamic dictionary requires at least 2^-26 log_2(1+n/(R+1)) expected-amortized cell probes per operation. The model permits fixed layouts of packed cells of at most one word each, including the short-spill convention used by succinct word-RAM structures, and covers zero-error Las Vegas algorithms with fresh per-invocation randomness and almost-sure termination. The proof repairs a conditioning defect in the inherited communication argument by placing pointwise probe caps inside the consistency event, then extends the lower bound to large universes through a scale-adaptive entropy parameter. Consequently, when U=2^w and n=ceil(w^c) for any fixed c>0, no always-correct predecessor structure can use log_2 binom(U,n)+o(n) persistent mutable bits and support constant-time operations. Constant expected-amortized time requires Omega(n) redundant bits. Lean 4 checks the complete packed-memory and fresh-random indexed models, hard distribution, communication bounds, separator, nested-forest accounting, deterministic and Las Vegas lower bounds, strict-predecessor reduction, and redundancy corollaries.

cs.DS↗

arXiv2026

An Exact Counterexample to Affine-Like Price-of-Anarchy Shape in Quartic BPR Routing

We give an exact computer-assisted counterexample to a direct common-degree quartic extension of the affine active-network shape theorem for demand-dependent Price of Anarchy. The instance is a directed network with five vertices, six edges, and three origin--destination paths, all with positive rational costs $c_e(x)=a_e+b_ex^4$. Exact rational interval certificates show that all three paths carry positive Wardrop flow throughout the demand interval $[17,24]$, while \[ \operatorname{PoA}(21)>\operatorname{PoA}(17),\qquad \operatorname{PoA}(21)>\operatorname{PoA}(24). \] Continuity therefore forces an interior local maximum despite a constant equilibrium active network. Krawczyk inclusions isolate the Wardrop and social-optimum KKT solutions, elementary boundary inequalities certify constant support, and interval social costs certify both strict comparisons. At differentiability points, we also derive a serial-edge identity explaining how a common quartic edge can alter the derivative of PoA without changing either route split. The proof and certificate use exact rational arithmetic for every interval and sign decision.

cs.GT↗

arXiv2026

A Tight Linear Deterministic Competitive Ratio for Fully Online KV-Cache Scheduling

Jaillet et al. introduced a fully online model for batching nonpreemptive LLM requests under a growing KV-cache memory constraint. For total end-to-end latency they proved that every deterministic algorithm has competitive ratio Omega(sqrt(n)), while the elementary sequential upper bound is n. We close this gap. Let R_det(n,M) be the optimal deterministic ratio for exactly n requests at memory M, and let R_det(n)=sup_M R_det(n,M). For every n >= 2 we prove (n-1)/12 <= R_det(n) <= n, so R_det(n)=Theta(n). The lower bound releases one memory-filling long request, observes its deterministic start time, and then releases n-1 wide one-token requests halfway through the long run. No short request can overlap the long one, whereas a hindsight schedule runs the two groups in the opposite order when useful. The hard instance uses the explicit fixed memory M=2(n-1)n. The upper bound is achieved by a uniform causal serial policy. The exact model, causality argument, both comparator branches, and quantifier order are machine-checked in Lean 4. Exact finite controls and replay commands accompany the proof.

cs.DS↗