A Bulk-Parallel Priority Queue in External Memory with STXXL

We propose the design and an implementation of a bulk-parallel external memory priority queue to take advantage of both shared-memory parallelism and high external memory transfer speeds to parallel disks. To achieve higher performance by decoupling item insertions and extractions, we offer two parallelization interfaces: one using "bulk" sequences, the other by defining "limit" items. In the design, we discuss how to parallelize insertions using multiple heaps, and how to calculate a dynamic prediction sequence to prefetch blocks and apply parallel multiway merge for extraction. Our experimental results show that in the selected benchmarks the priority queue reaches 75% of the full parallel I/O bandwidth of rotational disks and and 65% of SSDs, or the speed of sorting in external memory when bounded by computation.Comment: extended version of SEA'15 conference pape

Trip-Based Public Transit Routing

We study the problem of computing all Pareto-optimal journeys in a public transit network regarding the two criteria of arrival time and number of transfers taken. We take a novel approach, focusing on trips and transfers between them, allowing fine-grained modeling. Our experiments on the metropolitan network of London show that the algorithm computes full 24-hour profiles in 70 ms after a preprocessing phase of 30 s, allowing fast queries in dynamic scenarios.Comment: Minor corrections, no substantial changes. To be presented at ESA 201

Succinct Indices for Range Queries with applications to Orthogonal Range Maxima

We consider the problem of preprocessing $N$ points in 2D, each endowed with a priority, to answer the following queries: given a axis-parallel rectangle, determine the point with the largest priority in the rectangle. Using the ideas of the \emph{effective entropy} of range maxima queries and \emph{succinct indices} for range maxima queries, we obtain a structure that uses O(N) words and answers the above query in $O(\log N \log \log N)$ time. This is a direct improvement of Chazelle's result from FOCS 1985 for this problem -- Chazelle required $O(N/\epsilon)$ words to answer queries in $O((\log N)^{1+\epsilon})$ time for any constant $\epsilon > 0$.Comment: To appear in ICALP 201

Searching of gapped repeats and subrepetitions in a word

A gapped repeat is a factor of the form $uvu$ where $u$ and $v$ are nonempty words. The period of the gapped repeat is defined as $|u|+|v|$. The gapped repeat is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its period. The gapped repeat is called $\alpha$-gapped if its period is not greater than $\alpha |v|$. A $\delta$-subrepetition is a factor which exponent is less than 2 but is not less than $1+\delta$ (the exponent of the factor is the quotient of the length and the minimal period of the factor). The $\delta$-subrepetition is maximal if it cannot be extended to the left or to the right by at least one letter with preserving its minimal period. We reveal a close relation between maximal gapped repeats and maximal subrepetitions. Moreover, we show that in a word of length $n$ the number of maximal $\alpha$-gapped repeats is bounded by $O(\alpha^2n)$ and the number of maximal $\delta$-subrepetitions is bounded by $O(n/\delta^2)$. Using the obtained upper bounds, we propose algorithms for finding all maximal $\alpha$-gapped repeats and all maximal $\delta$-subrepetitions in a word of length $n$. The algorithm for finding all maximal $\alpha$-gapped repeats has $O(\alpha^2n)$ time complexity for the case of constant alphabet size and $O(n\log n + \alpha^2n)$ time complexity for the general case. For finding all maximal $\delta$-subrepetitions we propose two algorithms. The first algorithm has $O(\frac{n\log\log n}{\delta^2})$ time complexity for the case of constant alphabet size and $O(n\log n +\frac{n\log\log n}{\delta^2})$ time complexity for the general case. The second algorithm has $O(n\log n+\frac{n}{\delta^2}\log \frac{1}{\delta})$ expected time complexity

Activity of peroxisomal enzymes, and levels of polyamines in LPA-transgenic mice on two different diets

BACKGROUND: In man, elevated levels of plasma lipoprotein (a)(Lp(a)) is a cardiovascular risk factor, and oxidized phospholipids are believed to play a role as modulators of inflammatory processes such as atherosclerosis. Polyamines are potent antioxidants and anti-inflammatory agents. It was therefore of interest to examine polyamines and their metabolism in LPA transgenic mice. Concentration of the polyamines putrescine, spermidine and spermine as well as the activity of peroxisomal polyamine oxidase and two other peroxisomal enzymes, acyl-CoA oxidase and catalase were measured. The mice were fed either a standard diet or a diet high in fat and cholesterol (HFHC). Some of the mice in each feeding group were in addition given aminoguanidine (AG), a specific inhibitor of diamine oxidase, which catalyses degradation of putrescine, and also inhibits non-enzymatic glycosylation of protein which is implicated in the aetiology of atherosclerosis in diabetic patients. Non-transgenic mice were used as controls. RESULTS: Intestinal peroxisomal polyamine oxidase activity was significantly higher in LPA transgenic mice than in the non-transgenic mice, while intestinal peroxisomal catalase activity was significantly lower. Hepatic β-oxidation increased in Lp(a) transgenic mice fed the HFHC diet, but not in those on standard diet. Hepatic spermidine concentration was increased in all mice fed the HFHC diet compared to those fed a standard diet, while spermine concentration was decreased. With exception of the group fed only standard diet, transgenic mice showed a lower degree of hepatic steatosis than non-transgenic mice. AG had no significant effect on hepatic steatosis. CONCLUSION: The present results indicate a connection between peroxisomal enzyme activity and the presence of the human LPA gene in the murine genome. The effect may be a result of changes in oxidative processes in lipid metabolism rather than resulting from a direct effect of the LPA construct on the peroximal gene expression

Dictionary Matching with One Gap

The dictionary matching with gaps problem is to preprocess a dictionary $D$ of $d$ gapped patterns $P_1,\ldots,P_d$ over alphabet $\Sigma$, where each gapped pattern $P_i$ is a sequence of subpatterns separated by bounded sequences of don't cares. Then, given a query text $T$ of length $n$ over alphabet $\Sigma$, the goal is to output all locations in $T$ in which a pattern $P_i\in D$, $1\leq i\leq d$, ends. There is a renewed current interest in the gapped matching problem stemming from cyber security. In this paper we solve the problem where all patterns in the dictionary have one gap with at least $\alpha$ and at most $\beta$ don't cares, where $\alpha$ and $\beta$ are given parameters. Specifically, we show that the dictionary matching with a single gap problem can be solved in either $O(d\log d + |D|)$ time and $O(d\log^{\varepsilon} d + |D|)$ space, and query time $O(n(\beta -\alpha )\log\log d \log ^2 \min \{ d, \log |D| \} + occ)$, where $occ$ is the number of patterns found, or preprocessing time and space: $O(d^2 + |D|)$, and query time $O(n(\beta -\alpha ) + occ)$, where $occ$ is the number of patterns found. As far as we know, this is the best solution for this setting of the problem, where many overlaps may exist in the dictionary.Comment: A preliminary version was published at CPM 201

Succinct Data Structures for Families of Interval Graphs

We consider the problem of designing succinct data structures for interval graphs with $n$ vertices while supporting degree, adjacency, neighborhood and shortest path queries in optimal time in the $\Theta(\log n)$-bit word RAM model. The degree query reports the number of incident edges to a given vertex in constant time, the adjacency query returns true if there is an edge between two vertices in constant time, the neighborhood query reports the set of all adjacent vertices in time proportional to the degree of the queried vertex, and the shortest path query returns a shortest path in time proportional to its length, thus the running times of these queries are optimal. Towards showing succinctness, we first show that at least $n\log{n} - 2n\log\log n - O(n)$ bits are necessary to represent any unlabeled interval graph $G$ with $n$ vertices, answering an open problem of Yang and Pippenger [Proc. Amer. Math. Soc. 2017]. This is augmented by a data structure of size $n\log{n} +O(n)$ bits while supporting not only the aforementioned queries optimally but also capable of executing various combinatorial algorithms (like proper coloring, maximum independent set etc.) on the input interval graph efficiently. Finally, we extend our ideas to other variants of interval graphs, for example, proper/unit interval graphs, k-proper and k-improper interval graphs, and circular-arc graphs, and design succinct/compact data structures for these graph classes as well along with supporting queries on them efficiently

A Simple Linear-Space Data Structure for Constant-Time Range Minimum Query

Abstract. We revisit the range minimum query problem and present a new O(n)-space data structure that supports queries in O(1) time. Although previous data structures exist whose asymptotic bounds match ours, our goal is to introduce a new solution that is simple, intuitive, and practical without increasing asymptotic costs for query time or space

Encoding 2D Range Maximum Queries

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