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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.

The tremendous expanse of search engines, dictionary and thesaurus storage, and other text mining applications, combined with the popularity of readily available scanning devices and optical character recognition tools, has necessitated efficient storage, retrieval and management of massive text databases for various modern applications. For such applications, we propose a novel data structure, INSTRUCT, for efficient storage and management of sequence databases. Our structure uses bit vectors for reusing the storage space for common triplets, and hence, has a very low memory requirement. INSTRUCT efficiently handles prefix and suffix search queries in addition to the exact string search operation by iteratively checking the presence of triplets. We also propose an extension of the structure to handle substring search efficiently, albeit with an increase in the space requirements. This extension is important in the context of trie-based solutions which are unable to handle such queries efficiently. We perform several experiments portraying that INSTRUCT outperforms the existing structures by nearly a factor of two in terms of space requirements, while the query times are better. The ability to handle insertion and deletion of strings in addition to supporting all kinds of queries including exact search, prefix/suffix search and substring search makes INSTRUCT a complete data structure.

The field of succinct data structures has flourished over the last 16 years. Starting from the compressed suffix array (CSA) by Grossi and Vitter (STOC 2000) and the FM-index by Ferragina and Manzini (FOCS 2000), a number of generalizations and applications of string indexes based on the Burrows-Wheeler transform (BWT) have been developed, all taking an amount of space that is close to the input size in bits. In many large-scale applications, the construction of the index and its usage need to be considered as one unit of computation. Efficient string indexing and analysis in small space lies also at the core of a number of primitives in the data-intensive field of high-throughput DNA sequencing. We report the following advances in string indexing and analysis. We show that the BWT of a string $T\in \{1,\ldots,\sigma\}^n$ can be built in deterministic $O(n)$ time using just $O(n\log{\sigma})$ bits of space, where $\sigma \leq n$. Within the same time and space budget, we can build an index based on the BWT that allows one to enumerate all the internal nodes of the suffix tree of $T$. Many fundamental string analysis problems can be mapped to such enumeration, and can thus be solved in deterministic $O(n)$ time and in $O(n\log{\sigma})$ bits of space from the input string. We also show how to build many of the existing indexes based on the BWT, such as the CSA, the compressed suffix tree (CST), and the bidirectional BWT index, in randomized $O(n)$ time and in $O(n\log{\sigma})$ bits of space. The previously fastest construction algorithms for BWT, CSA and CST, which used $O(n\log{\sigma})$ bits of space, took $O(n\log{\log{\sigma}})$ time for the first two structures, and $O(n\log^{\epsilon}n)$ time for the third, where $\epsilon$ is any positive constant. Contrary to the state of the art, our bidirectional BWT index supports every operation in constant time per element in its output.

The field of succinct data structures has flourished over the last 16 years. Starting from the compressed suffix array (CSA) by Grossi and Vitter (STOC 2000) and the FM-index by Ferragina and Manzini (FOCS 2000), a number of generalizations and applications of string indexes based on the Burrows-Wheeler transform (BWT) have been developed, all taking an amount of space that is close to the input size in bits. In many large-scale applications, the construction of the index and its usage need to be considered as one unit of computation. Efficient string indexing and analysis in small space lies also at the core of a number of primitives in the data-intensive field of high-throughput DNA sequencing. We report the following advances in string indexing and analysis. We show that the BWT of a string $T\in \{1,\ldots,\sigma\}^n$ can be built in deterministic $O(n)$ time using just $O(n\log{\sigma})$ bits of space, where $\sigma \leq n$. Within the same time and space budget, we can build an index based on the BWT that allows one to enumerate all the internal nodes of the suffix tree of $T$. Many fundamental string analysis problems can be mapped to such enumeration, and can thus be solved in deterministic $O(n)$ time and in $O(n\log{\sigma})$ bits of space from the input string. We also show how to build many of the existing indexes based on the BWT, such as the CSA, the compressed suffix tree (CST), and the bidirectional BWT index, in randomized $O(n)$ time and in $O(n\log{\sigma})$ bits of space. The previously fastest construction algorithms for BWT, CSA and CST, which used $O(n\log{\sigma})$ bits of space, took $O(n\log{\log{\sigma}})$ time for the first two structures, and $O(n\log^{\epsilon}n)$ time for the third, where $\epsilon$ is any positive constant. Contrary to the state of the art, our bidirectional BWT index supports every operation in constant time per element in its output.

We consider the problem of indexing a string $t$ of length $n$ to report the occurrences of a query pattern $p$ containing $m$ characters and $j$ wildcards. Let $occ$ be the number of occurrences of $p$ in $t$, and $\sigma$ the size of the alphabet. We obtain the following results. - A linear space index with query time $O(m+\sigma^j \log \log n + occ)$. This significantly improves the previously best known linear space index by Lam et al. [ISAAC 2007], which requires query time $\Theta(jn)$ in the worst case. - An index with query time $O(m+j+occ)$ using space $O(\sigma^{k^2} n \log^k \log n)$, where $k$ is the maximum number of wildcards allowed in the pattern. This is the first non-trivial bound with this query time. - A time-space trade-off, generalizing the index by Cole et al. [STOC 2004]. We also show that these indexes can be generalized to allow variable length gaps in the pattern. Our results are obtained using a novel combination of well-known and new techniques, which could be of independent interest.

1Our Atomic World: The Story of Atomic Energy

By C. Jackson Craven

This booklet is part of the "Understanding the Atom Series" published by the Division of Technical Information of the U.S. Atomic Energy Commission. From an introduction of atomic theory by the ancient Greeks through the development of the fission bomb, the author covers such areas as the discovery of the nucleus, the discovery of isotopes, fission and fusion including a chronology of atomic theory to 1963, and the development of the Atomic Energy Commission. (Summary by Larry Wilson)