Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1102.4480

LGM: Mining Frequent Subgraphs from Linear Graphs

Yasuo Tabei·Daisuke Okanohara·Shuichi Hirose·Koji Tsuda
View original source ↗Read source document ↗Export metadata ↓

Abstract

A linear graph is a graph whose vertices are totally ordered. Biological and linguistic sequences with interactions among symbols are naturally represented as linear graphs. Examples include protein contact maps, RNA secondary structures and predicate-argument structures. Our algorithm, linear graph miner (LGM), leverages the vertex order for efficient enumeration of frequent subgraphs. Based on the reverse search principle, the pattern space is systematically traversed without expensive duplication checking. Disconnected subgraph patterns are particularly important in linear graphs due to their sequential nature. Unlike conventional graph mining algorithms detecting connected patterns only, LGM can detect disconnected patterns as well. The utility and efficiency of LGM are demonstrated in experiments on protein contact maps.

Explore related subjects

cs.DS

Keep this discovery

BibTeXRIS

Yasuo Tabei, Daisuke Okanohara, Shuichi Hirose, Koji Tsuda. 2011-02-22. LGM: Mining Frequent Subgraphs from Linear Graphs. https://arxiv.org/abs/1102.4480

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗
arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗