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The graph edit distance (GED) is a well-established distance measure widely used in many applications. However, existing methods for the GED computation suffer from several drawbacks including oversized search space, huge memory consumption, and lots of expensive backtracking. In this paper, we present BSS_GED, a novel vertex-based mapping method for the GED computation. First, we create a small search space by reducing the number of invalid and redundant mappings involved in the GED computation. Then, we utilize beam-stack search combined with two heuristics to efficiently compute GED, achieving a flexible trade-off between available memory and expensive backtracking. Extensive experiments demonstrate that BSS GED is highly efficient for the GED computation on sparse as well as dense graphs and outperforms the state-of-the-art GED methods. In addition, we also apply BSS_GED to the graph similarity search problem and the practical results confirm its efficiency.

In the dynamic indexing problem, we must maintain a changing collection of text documents so that we can efficiently support insertions, deletions, and pattern matching queries. We are especially interested in developing efficient data structures that store and query the documents in compressed form. All previous compressed solutions to this problem rely on answering rank and select queries on a dynamic sequence of symbols. Because of the lower bound in [Fredman and Saks, 1989], answering rank queries presents a bottleneck in compressed dynamic indexing. In this paper we show how this lower bound can be circumvented using our new framework. We demonstrate that the gap between static and dynamic variants of the indexing problem can be almost closed. Our method is based on a novel framework for adding dynamism to static compressed data structures. Our framework also applies more generally to dynamizing other problems. We show, for example, how our framework can be applied to develop compressed representations of dynamic graphs and binary relations.

In this paper we describe compressed indexes that support pattern matching queries for strings with wildcards. For a constant size alphabet our data structure uses $O(n\log^{\varepsilon}n)$ bits for any $\varepsilon>0$ and reports all $\mathrm{occ}$ occurrences of a wildcard string in $O(m+\sigma^g \cdot\mu(n) + \mathrm{occ})$ time, where $\mu(n)=o(\log\log\log n)$, $\sigma$ is the alphabet size, $m$ is the number of alphabet symbols and $g$ is the number of wildcard symbols in the query string. We also present an $O(n)$-bit index with $O((m+\sigma^g+\mathrm{occ})\log^{\varepsilon}n)$ query time and an $O(n(\log\log n)^2)$-bit index with $O((m+\sigma^g+\mathrm{occ})\log\log n)$ query time. These are the first non-trivial data structures for this problem that need $o(n\log n)$ bits of space., Comment: 15 pages, extended version of the STACS paper

Color (or categorical) range reporting is a variant of the orthogonal range reporting problem in which every point in the input is assigned a \emph{color}. While the answer to an orthogonal point reporting query contains all points in the query range $Q$, the answer to a color reporting query contains only distinct colors of points in $Q$. In this paper we describe an O(N)-space data structure that answers one-dimensional color reporting queries in optimal $O(k+1)$ time, where $k$ is the number of colors in the answer and $N$ is the number of points in the data structure. Our result can be also dynamized and extended to the external memory model.

Let ${\cal{D}}$ = $\{d_1, d_2, d_3, ..., d_D\}$ be a given set of $D$ (string) documents of total length $n$. The top-$k$ document retrieval problem is to index $\cal{D}$ such that when a pattern $P$ of length $p$, and a parameter $k$ come as a query, the index returns the $k$ most relevant documents to the pattern $P$. Hon et. al. \cite{HSV09} gave the first linear space framework to solve this problem in $O(p + k\log k)$ time. This was improved by Navarro and Nekrich \cite{NN12} to $O(p + k)$. These results are powerful enough to support arbitrary relevance functions like frequency, proximity, PageRank, etc. In many applications like desktop or email search, the data resides on disk and hence disk-bound indexes are needed. Despite of continued progress on this problem in terms of theoretical, practical and compression aspects, any non-trivial bounds in external memory model have so far been elusive. Internal memory (or RAM) solution to this problem decomposes the problem into $O(p)$ subproblems and thus incurs the additive factor of $O(p)$. In external memory, these approaches will lead to $O(p)$ I/Os instead of optimal $O(p/B)$ I/O term where $B$ is the block-size. We re-interpret the problem independent of $p$, as interval stabbing with priority over tree-shaped structure. This leads us to a linear space index in external memory supporting top-$k$ queries (with unsorted outputs) in near optimal $O(p/B + \log_B n + \log^{(h)} n + k/B)$ I/Os for any constant $h${$\log^{(1)}n =\log n$ and $\log^{(h)} n = \log (\log^{(h-1)} n)$}. Then we get $O(n\log^*n)$ space index with optimal $O(p/B+\log_B n + k/B)$ I/Os., Comment: 3 figures