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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
The Complexity of Approximate Pattern Matching on De Brui...
Daniel Gibney, Sharma V. Thankachan, Srinivas Aluru · 2022-01-29 · via cs.DS updates on arXiv.org

Aligning a sequence to a walk in a labeled graph is a problem of fundamental importance to Computational Biology. For finding a walk in an arbitrary graph with $|E|$ edges that exactly matches a pattern of length $m$, a lower bound based on the Strong Exponential Time Hypothesis (SETH) implies an algorithm significantly faster than $O(|E|m)$ time is unlikely [Equi et al., ICALP 2019]. However, for many special graphs, such as de Bruijn graphs, the problem can be solved in linear time [Bowe et al., WABI 2012]. For approximate matching, the picture is more complex. When edits (substitutions, insertions, and deletions) are only allowed to the pattern, or when the graph is acyclic, the problem is again solvable in $O(|E|m)$ time. When edits are allowed to arbitrary cyclic graphs, the problem becomes NP-complete, even on binary alphabets [Jain et al., RECOMB 2019]. These results hold even when edits are restricted to only substitutions. The complexity of approximate pattern matching on de Bruijn graphs remained open. We investigate this problem and show that the properties that make de Bruijn graphs amenable to efficient exact pattern matching do not extend to approximate matching, even when restricted to the substitutions only case with alphabet size four. We prove that determining the existence of a matching walk in a de Bruijn graph is NP-complete when substitutions are allowed to the graph. In addition, we demonstrate that an algorithm significantly faster than $O(|E|m)$ is unlikely for de Bruijn graphs in the case where only substitutions are allowed to the pattern. This stands in contrast to pattern-to-text matching where exact matching is solvable in linear time, like on de Bruijn graphs, but approximate matching under substitutions is solvable in subquadratic $O(n\sqrt{m})$ time, where $n$ is the text's length [Abrahamson, SIAM J. Computing 1987].