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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Evaluating Optimal Safe Flows Decomposition for RNA Assembly
Bashar Ahmed, Siddharth Singh Rana, Ujjwal, Shahbaz Khan · 2024-09-20 · via cs.DS updates on arXiv.org

In Bioinformatics, the applications of flow decomposition in directed acyclic graphs are highlighted in RNA Assembly problem. However, it admits multiple solutions where exactly one solution correctly represents the underlying transcripts. The problem was addressed by Safe and Complete framework~[RECOMB16], which reports all the parts of the solution that are present in every possible solution. Khan et al.~[RECOMB22] first studied flow decomposition in the safe and complete framework. Their algorithm showed superior performance ($\approx20\%$) over the popular heuristic (greedy-width) on sufficiently complex graphs for a unified metric of precision and coverage (F-score). They presented the solution in multiple representations using simple but suboptimal algorithms, which were later optimized by Khan and Tomescu~[ESA22], who also presented an optimal representation. In this paper, we evaluate the practical significance of the optimal algorithms by Khan and Tomescu~[ESA22]. Our work highlights the significance of the theoretically optimal algorithms improving time (up to $60-70\%$) and memory (up to $76-85\%$), and the optimal representations improving output size (up to $135-170\%$) significantly. However, the impact of optimal algorithms was limited due to a large number of extremely short safe paths. We propose heuristics to improve these representations further, resulting in further improvement in time (up to $10\%$) and output size ($10-25\%$). However, in absolute terms, these improvements were limited to a few seconds on real datasets involved due to the smaller size of the graphs. We thus generated large random graphs, to demonstrate the scalability of the above results. The older algorithms [RECOMB22] were not practical on moderately large graphs ($\geq 1M$ nodes), while optimal algorithms [ESA22] were linearly scalable for much larger graphs ($\geq 100M$ nodes).