arXiv subjects

Hiroki Arimura

Publications and source records attributed to Hiroki Arimura.

22 records · Page 2Linked to original sources

arXiv2017

Linear-size CDAWG: new repetition-aware indexing and grammar compression

In this paper, we propose a novel approach to combine \emph{compact directed acyclic word graphs} (CDAWGs) and grammar-based compression. This leads us to an efficient self-index, called Linear-size CDAWGs (L-CDAWGs), which can be represented with $O(\tilde e_T \log n)$ bits of space allowing for $O(\log n)$-time random and $O(1)$-time sequential accesses to edge labels, and $O(m \log σ+ occ)$-time pattern matching. Here, $\tilde e_T$ is the number of all extensions of maximal repeats in $T$, $n$ and $m$ are respectively the lengths of the text $T$ and a given pattern, $σ$ is the alphabet size, and $occ$ is the number of occurrences of the pattern in $T$. The repetitiveness measure $\tilde e_T$ is known to be much smaller than the text length $n$ for highly repetitive text. For constant alphabets, our L-CDAWGs achieve $O(m + occ)$ pattern matching time with $O(e_T^r \log n)$ bits of space, which improves the pattern matching time of Belazzougui et al.'s run-length BWT-CDAWGs by a factor of $\log \log n$, with the same space complexity. Here, $e_T^r$ is the number of right extensions of maximal repeats in $T$. As a byproduct, our result gives a way of constructing an SLP of size $O(\tilde e_T)$ for a given text $T$ in $O(n + \tilde e_T \log σ)$ time.

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arXiv2017

Efficient Enumeration of Induced Matchings in a Graph without Cycles with Length Four

We address the induced matching enumeration problem. An edge set $M$ is an induced matching of a graph $G =(V,E)$. The enumeration of matchings are widely studied in literature, but the induced matching has not been paid much attention. A straightforward algorithm takes $O(|V|)$ time for each solution, that is coming from the time to generate a subproblem. We investigated local structures that enables us to generate subproblems in short time, and proved that the time complexity will be $O(1)$ if the input graph is $C_4$-free. A $C_4$-free graph is a graph any whose subgraph is not a cycle of length four. Finally, we show the fixed parameter tractability of counting induced matchings for graphs with bounded tree-width and planar graphs.

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arXiv2016

Packed Compact Tries: A Fast and Efficient Data Structure for Online String Processing

In this paper, we present a new data structure called the packed compact trie (packed c-trie) which stores a set $S$ of $k$ strings of total length $n$ in $n \logσ+ O(k \log n)$ bits of space and supports fast pattern matching queries and updates, where $σ$ is the size of an alphabet. Assume that $α= \log_σn$ letters are packed in a single machine word on the standard word RAM model, and let $f(k,n)$ denote the query and update times of the dynamic predecessor/successor data structure of our choice which stores $k$ integers from universe $[1,n]$ in $O(k \log n)$ bits of space. Then, given a string of length $m$, our packed c-tries support pattern matching queries and insert/delete operations in $O(\frac{m}α f(k,n))$ worst-case time and in $O(\frac{m}α + f(k,n))$ expected time. Our experiments show that our packed c-tries are faster than the standard compact tries (a.k.a. Patricia trees) on real data sets. As an application of our packed c-trie, we show that the sparse suffix tree for a string of length $n$ over prefix codes with $k$ sampled positions, such as evenly-spaced and word delimited sparse suffix trees, can be constructed online in $O((\frac{n}α + k) f(k,n))$ worst-case time and $O(\frac{n}α + k f(k,n))$ expected time with $n \log σ+ O(k \log n)$ bits of space. When $k = O(\frac{n}α)$, by using the state-of-the-art dynamic predecessor/successor data structures, we obtain sub-linear time construction algorithms using only $O(\frac{n}α)$ bits of space in both cases. We also discuss an application of our packed c-tries to online LZD factorization.

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arXiv2014

Efficient Enumeration of Induced Subtrees in a K-Degenerate Graph

In this paper, we address the problem of enumerating all induced subtrees in an input k-degenerate graph, where an induced subtree is an acyclic and connected induced subgraph. A graph G = (V, E) is a k-degenerate graph if for any its induced subgraph has a vertex whose degree is less than or equal to k, and many real-world graphs have small degeneracies, or very close to small degeneracies. Although, the studies are on subgraphs enumeration, such as trees, paths, and matchings, but the problem addresses the subgraph enumeration, such as enumeration of subgraphs that are trees. Their induced subgraph versions have not been studied well. One of few example is for chordless paths and cycles. Our motivation is to reduce the time complexity close to O(1) for each solution. This type of optimal algorithms are proposed many subgraph classes such as trees, and spanning trees. Induced subtrees are fundamental object thus it should be studied deeply and there possibly exist some efficient algorithms. Our algorithm utilizes nice properties of k-degeneracy to state an effective amortized analysis. As a result, the time complexity is reduced to O(k) time per induced subtree. The problem is solved in constant time for each in planar graphs, as a corollary.

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