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

Exploring the cost-effectiveness of high versus low perioperative fraction of inspired oxygen in the prevention of surgical site infections among abdominal surgery patients in three low- and middle-income countries

Background: This study assessed the potential cost-effectiveness of high (80–100%) vs low (21–35%) fraction of inspired oxygen (FiO2) at preventing surgical site infections (SSIs) after abdominal surgery in Nigeria, India, and South Africa. Methods: Decision-analytic models were constructed using best available evidence sourced from unbundled data of an ongoing pilot trial assessing the effectiveness of high FiO2, published literature, and a cost survey in Nigeria, India, and South Africa. Effectiveness was measured as percentage of SSIs at 30 days after surgery, a healthcare perspective was adopted, and costs were reported in US dollars ($). Results: High FiO2 may be cost-effective (cheaper and effective). In Nigeria, the average cost for high FiO2 was$216 compared with $222 for low FiO2 leading to a −$6 (95% confidence interval [CI]: −$13 to −$1) difference in costs. In India, the average cost for high FiO2 was $184 compared with$195 for low FiO2 leading to a −$11 (95$15 to −$6) difference in costs. In South Africa, the average cost for high FiO2 was$1164 compared with $1257 for low FiO2 leading to a −$93 (95% CI: −$132 to −$65) difference in costs. The high FiO2 arm had few SSIs, 7.33% compared with 8.38% for low FiO2, leading to a −1.05 (95% CI: −1.14 to −0.90) percentage point reduction in SSIs. Conclusion: High FiO2 could be cost-effective at preventing SSIs in the three countries but further data from large clinical trials are required to confirm this