For more than 20 years, the Model-RB benchmark frb100-40 remained an open challenge; since 2014, its public record had stood at 99 of 100 variables. We give a directly checkable 100-vertex independent set for its 4,000-vertex graph. Together with a verified partition into 100 cliques of size 40, the witness proves that the maximum independent-set size is 100 and the minimum vertex-cover size is 3,900. The stochastic run that found the witness is kept separate from this proof. We evaluated its added pair and triple repair operators in a preregistered campaign comprising 8,668 valid runs. The primary comparison found no detectable acceleration over base ULSA (hazard ratio 0.967, 95% confidence interval 0.915-1.023; p=0.248), and the factorial ablation reached the same conclusion. On a smaller FRB suite, the group-aware CSP pipeline solved 2,500/2,500 runs, compared with 2,391/2,500 for LibMVC-NuMVC. On frb100-40, full ULSA, base ULSA, and NuMVC each produced 0/56 new certificates. With no events, the planned cross-solver hazard ratios remain unidentified. NuMVC ended with cover size 3,902 in 40 runs and 3,903 in 16. Exhaustive enumeration showed that none of the 108 unique recorded conflict-two states had a strictly improving group-aware CSP neighbor within Hamming radius three. The certificate settles the instance. The experiments characterize the search barrier, and the preregistered comparisons show no heuristic advantage.
A durable assumption holds that graph analytics requires a purpose-built graph engine, and that relational systems are ill-suited to connected data. We argue the opposite for the workloads enterprises actually run. A columnar relational engine fronted by a graph query language matches or exceeds native graph engines on analytical graph queries, and - decisively - scales past the point where in-memory graph engines fail. We further argue that the node/edge property graph is not a more faithful model of connected data but a re-encoding of relationships that already exist explicitly in relational tables; reconstructing them at query time is pure overhead. We present ClickGraph and its Databricks-dialect sibling DeltaGraph, systems that translate Cypher directly onto the native relational schema - the tables, columns, and foreign keys as they already exist - and execute in place on ClickHouse, Databricks, or in-process on lakehouse files, with no import and no separate cluster. Because the output is ordinary SQL, an underperforming query is an open optimization surface: it can be rewritten, and the engine itself extended. We support the argument with a peer system's own published benchmark, in which a columnar engine outruns Neo4j by two-to-four orders of magnitude, and with reproducible measurements across the LDBC Social Network Benchmark suite.
Continuous optimisation methods need to balance sharing information and maintaining alternative search directions. In this paper, we introduce Mycelial Search (Myco), a graph-structured metaheuristic designed around active tips, community-weighted flow, adaptive cord plasticity, and anchor-based injection. Candidate solutions form an evolving spatial graph in which a Louvain partition distinguishes within-community from cross-community information exchange. Adaptive cord plasticity subsequently modifies active tip-to-tip edges according to their alignment with the local flow. An anchor-based injection mechanism supplements the graph-driven tip dynamics. We evaluated Myco on the CEC 2022 single-objective bound-constrained benchmark suite at dimensions $D=10$ and $D=20$, using 30 independent runs per algorithm-function pair. The comparison includes eleven established optimisers from several search families. Myco reaches competitive results on selected functions across both dimensions. The ablation analysis further shows that community structure regulates the range of graph-based information exchange, whereas cord plasticity controls the persistence of local directional influence. These findings indicate that graph-structured local interaction can support continuous optimisation, while its effectiveness depends on landscape structure and information transfer across local search regions.
Benchmarks can run without determining what their results license. We freeze a large evaluation collection and attempt to replay its historical claims. Most units stop because the evidence required for replay is not bound. Where replay is possible, different claims remain stable at different resolutions. We make this otherwise implicit inference step explicit and executable.
Andrew Soroka, German Mikhelson, Alexander Mescheryakov +1cs.LG
The problem of route optimization with realistic constraints is becoming extremely relevant in the face of global urban population growth. While we are aware of approaches that theoretically provide an exact optimal solution, their application becomes challenging as the problem size increases because of exponential complexity. We investigate the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and compare solutions obtaining by exact solver SCIP with heuristic algorithms such as LKH, 2-OPT, 3-OPT, the ORTools framework, and the deep learning model JAMPR. We demonstrate that for problem of size 50 deep learning and classical heuristic solutions became close to SCIP exact solution but requires less time. Additionally for problems with size 100, SCIP exact methods around 13 times slower that neural and classical heuristics with the same route cost and on around 50% worse for the first feasible solution on the same time. To conduct experiments, we developed the Smart Routes platform for solving route optimization problems, which includes exact, heuristic, and deep learning models, and facilitates convenient integration of custom algorithms and datasets.
Swarm and evolutionary algorithms are usually analyzed as complete procedural systems in which nonlinear selection, replacement, and adaptation obscure simpler structure within candidate generation. This paper introduces an operator--selection factorization that separates objective-independent variation from boundary repair and fitness-dependent selection, and uses it to study the proposal geometry of the Self-Organizing Migrating Algorithm (SOMA) and Differential Evolution (DE). The canonical SOMA proposal is shown to be affine in the search space and exactly linear in an augmented migrant--leader state. In leader-relative coordinates, the resulting operator provides a direct interpretation of interpolation, projection, overshooting, and coordinate masking. Under Bernoulli perturbation masks, we derive closed-form expressions for the proposal mean, covariance, expected squared step length, expected squared distance from the leader, active dimensionality, and coordinate coverage. For canonical DE/rand/1/bin, we derive the finite-population moments of differential mutation and characterize the additional covariance and coordinate dependence induced by forced-coordinate binomial crossover. Exact enumeration and Monte Carlo experiments verify the analytical identities and quantify the effects of mask conditioning, boundary repair, and fitness-based selection. The analysis further motivates geometry-controlled and rotation-aware SOMA variants, together with an adaptive population-reducing extension of iSOMA. Experiments on the complete noiseless BBOB benchmark show that these operator-guided variants substantially improve upon canonical SOMA and are competitive with established DE methods in several dimension--budget regimes. The results demonstrate how proposal-level operator analysis can support both the interpretation and design of population-based optimizers.
Time-dependent routing recognizes that the same journey can take a different time depending on when it begins. Under duration minimization, even the departure time of each vehicle becomes a decision. Exact methods for this setting exist in the literature, but researchers and practitioners have lacked a ready-to-use open solver that combines rich piecewise-linear travel times, early feasible solutions and optimality claims. KAYROS fills this gap with two modes on one checker-consistent engine: an Iterated Local Search that streams improving solutions and a Branch-Price-and-Cut method that can issue computational optimality certificates under explicit arithmetic and search assumptions. It installs with one command and has no proprietary dependency. The public MAMUT-routing store currently contains 704 KAYROS certificates under a four-solve publication protocol, which has also led to the retraction and repair of invalid earlier claims. The report presents two complementary benchmark contributions to MAMUT-routing. The first integrates Blauth2024, a benchmark from the literature whose travel times derive from measured Uber speeds, for which KAYROS provides new best-known solutions on all 40 instances. The second proposes Poryos2026, a new benchmark of 1,080 paired static and time-dependent instances built from OpenStreetMap road networks and controlled synthetic traffic. Finally, the report describes the intensive human-AI collaboration behind this work and the verification practices that kept its outputs independently verifiable.
Lance Kennedy, Hossein Amiri, Yueyang Liu +9cs.LG cs.CG
Detecting staypoints from raw trajectory data is fundamental to numerous spatial computing applications. This process transforms raw numeric sequences of geolocations into semantically meaningful locations, such as homes, workplaces, or restaurants. Despite its importance for semantic trajectory analysis, staypoint detection lacks standard benchmarks, and existing algorithms have never been systematically evaluated. This gap persists because no publicly available datasets provide both raw individual trajectories and ground-truth staypoint annotations. This benchmark paper addresses this limitation with two key contributions: (1) we introduce 16 large-scale simulated datasets capturing thousands of agents with annotated staypoints across varying trajectory noise levels, and (2) we evaluate nine staypoint detection algorithms-including both state-of-the-art and novel methods-to analyze their robustness to noise. Our evaluation reveals that existing state-of-the-art algorithms perform poorly under realistic noise conditions. Conversely, our proposed unsupervised methods yield substantial improvements, while supervised approaches drastically outperform existing baselines. While these results are very promising, these datasets and methods are only meant as starting points for future research in staypoint detection.
Taebong Kim, Youngsik Hong, Minsik Kim +4cs.CR cs.AI
We report genuine-un-compiled, textbook-faithful-quantum cryptanalysis of symmetric-cipher structures executed on real IBM quantum hardware (ibm\_kingston, Heron generation). Using Simon's algorithm we recover the hidden period of the Even-Mansour cipher up to security parameter N = 10 on real hardware, beyond the largest previously reported real-hardware key recovery of N = 4, and we cleanly recover the periods of a 3-round Feistel (DES-family) construction at block sizes 6 and 8; a 21-qubit block-10 instance is verified in simulation and submitted to hardware. We further provide a breadth-first benchmark of five genuine quantum attacks spanning four symmetric-cipher design paradigms -- Bernstein-Vazirani (linear structure, single query), Grover (SPN key search, quadratic), and Simon (Even-Mansour, CBC-MAC forgery, and Feistel; exponential-to-polynomial in query complexity) -- validated to the classical-simulation ceiling of 25 qubits. We are deliberately explicit about scope: these attacks target reduced or structured constructions in the Q2 (quantum-query) model, asymptotically follow the birthday bound and therefore do not constitute quantum advantage over classical collision-finding, do not break full AES/RSA or 16-round DES, and rely on error mitigation rather than fault-tolerant error correction. Our contribution is the real-hardware demonstration at record structure sizes, the breadth of genuine algorithmic coverage across four paradigms, and an honest, reproducible benchmark with public artifacts.
Sampling from discrete Markov random fields (MRFs) is a hard problem. We study amplitude-encoded i.i.d. sampling for small MRFs where $2^n$ target probabilities are precomputed classically. This removes quantum exponential speedup but allows a clean comparison against classical MCMC based on independent circuit samples ($τ\approx 1$). Across 60 instances spanning five graph families (1k-step burn-in, 3k retained samples), the mean ESS ratios of Quantum to Single-Site Gibbs, Block Gibbs, Tuned-Block, and Parallel Tempering are $16.35$, $7.29$, $1.82$, and $1.79$, showing modern classical samplers substantially close this gap. Amortizing $O(2^n)$ preprocessing into wall-clock time, exact inverse-CDF sampling yields $17.7\text{M}$ ESS/s versus $488\text{K}$ ESS/s for the quantum sampler ($36\times$ mean rate, $153\times$ per-instance), confirming no wall-clock advantage. We characterize MCMC autocorrelation costs and benchmark amplitude-encoded state preparation at $n \in \{8,10,12\}$. An MPS scaling study ($n \le 40$) shows bond dimension $χ=32$ achieves $F=0.721\pm0.059$ at $n=40$. Finally, a matched-budget VQC vs. MPS comparison at $n \in \{8,10,12\}$ shows VQC fidelities fall far below MPS: $(F_{\mathrm{VQC}}, F_{\mathrm{MPS}}) = (0.31, 0.99), (0.21, 0.96), (0.17, 0.88)$ at compressions $10.7\times$, $34.1\times$, and $113.8\times$.
Jiayang Niu, Akib Karim, Yan Wang +5quant-ph cs.AI
Quantum Architecture Search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms, yet existing benchmarks organize instances by molecular identity or qubit count -- criteria agnostic to Hamiltonian structure -- and rely solely on energy accuracy, which cannot detect structural failures such as over-parameterization on near-product ground states. We introduce HamQASBench, a Hamiltonian-informed diagnostic benchmark organizing 11 molecules into five structural tiers via fingerprints derived from the Pauli operator basis, computational basis representation, and ground-state entanglement. A post-hoc critical-structure extraction procedure identifies minimal circuits consistent with each tier's requirements, complementing energy-based evaluation with per-qubit entanglement analysis and pairwise state fidelity. Benchmarking five QAS methods across four paradigms reveals failure modes invisible to conventional metrics: over-parameterization in the minimalism regime, eigenstate commitment under degeneracy, a representation bottleneck in strongly correlated systems, topology-induced routing failure, and circuit search space growth as a scalability bottleneck.