New Algorithms for Position Heaps

We present several results about position heaps, a relatively new alternative to suffix trees and suffix arrays. First, we show that, if we limit the maximum length of patterns to be sought, then we can also limit the height of the heap and reduce the worst-case cost of insertions and deletions. Second, we show how to build a position heap in linear time independent of the size of the alphabet. Third, we show how to augment a position heap such that it supports access to the corresponding suffix array, and vice versa. Fourth, we introduce a variant of a position heap that can be simulated efficiently by a compressed suffix array with a linear number of extra bits

Efficient Seeds Computation Revisited

The notion of the cover is a generalization of a period of a string, and there are linear time algorithms for finding the shortest cover. The seed is a more complicated generalization of periodicity, it is a cover of a superstring of a given string, and the shortest seed problem is of much higher algorithmic difficulty. The problem is not well understood, no linear time algorithm is known. In the paper we give linear time algorithms for some of its versions --- computing shortest left-seed array, longest left-seed array and checking for seeds of a given length. The algorithm for the last problem is used to compute the seed array of a string (i.e., the shortest seeds for all the prefixes of the string) in $O(n^2)$ time. We describe also a simpler alternative algorithm computing efficiently the shortest seeds. As a by-product we obtain an $O(n\log{(n/m)})$ time algorithm checking if the shortest seed has length at least $m$ and finding the corresponding seed. We also correct some important details missing in the previously known shortest-seed algorithm (Iliopoulos et al., 1996).Comment: 14 pages, accepted to CPM 201

A sudden presentation of abdominal compartment syndrome

Dear Editor, Abdominal compartment syndrome (ACS) is defined as sustained intra-abdominal pressure (IAP) exceeding 20 mm Hg, which causes end-organ damage due to impaired tissue perfusion, as with other compartment syndromes [1, 2]. This dysfunction can extend beyond the abdomen to other organs like the heart and lungs. ACS is most commonly caused by trauma or surgery to the abdomen. It is characterised by interstitial oedema, which can be exacerbated by large fluid shifts during massive transfusion of blood products and other fluid resuscitation [3]. Normally, IAP is nearly equal to or slightly above ambient pressure. Intra-abdominal hypertension is typically defined as abdominal pressure greater than or equal to 12 mm Hg [4]. Initially, the abdomen is able to distend to accommodate the increase in pressure caused by oedema; however, IAP becomes highly sensitive to any additional volume once maximum distension is reached. This is a function of abdominal compliance, which plays a key role in the development and progression of intra-abdominal hypertension [5]. Surgical decompression is required in severe cases of organ dysfunction – usually when IAPs are refractory to other treatment options [6]. Excessive abdominal pressure leads to systemic pathophysiological consequences that may warrant admission to a critical care unit. These include hypoventilation secondary to restriction of the deflection of the diaphragm, which results in reduced chest wall compliance. This is accompanied by hypoxaemia, which is exacerbated by a decrease in venous return. Combined, these consequences lead to decreased cardiac output, a V/Q mismatch, and compromised perfusion to intra-abdominal organs, most notably the kidneys [7]. Kidney damage can be prerenal due to renal vein or artery compression, or intrarenal due to glomerular compression [8] – both share decreased urine output as a manifestation. Elevated bladder pressure is also seen from compression due to increased abdominal pressure, and its measurement, via a Foley catheter, is a diagnostic hallmark. Sustained intra-bladder pressures beyond 20 mm Hg with organ dysfunction are indicative of ACS requiring inter­vention [2, 8]. ACS is an important aetiology to consider in the differential diagnosis for signs of organ dysfunction – especially in the perioperative setting – as highlighted in the case below

Efficient LZ78 factorization of grammar compressed text

We present an efficient algorithm for computing the LZ78 factorization of a text, where the text is represented as a straight line program (SLP), which is a context free grammar in the Chomsky normal form that generates a single string. Given an SLP of size $n$ representing a text $S$ of length $N$, our algorithm computes the LZ78 factorization of $T$ in $O(n\sqrt{N}+m\log N)$ time and $O(n\sqrt{N}+m)$ space, where $m$ is the number of resulting LZ78 factors. We also show how to improve the algorithm so that the $n\sqrt{N}$ term in the time and space complexities becomes either $nL$, where $L$ is the length of the longest LZ78 factor, or $(N - \alpha)$ where $\alpha \geq 0$ is a quantity which depends on the amount of redundancy that the SLP captures with respect to substrings of $S$ of a certain length. Since $m = O(N/\log_\sigma N)$ where $\sigma$ is the alphabet size, the latter is asymptotically at least as fast as a linear time algorithm which runs on the uncompressed string when $\sigma$ is constant, and can be more efficient when the text is compressible, i.e. when $m$ and $n$ are small.Comment: SPIRE 201

One-variable word equations in linear time

In this paper we consider word equations with one variable (and arbitrary many appearances of it). A recent technique of recompression, which is applicable to general word equations, is shown to be suitable also in this case. While in general case it is non-deterministic, it determinises in case of one variable and the obtained running time is O(n + #_X log n), where #_X is the number of appearances of the variable in the equation. This matches the previously-best algorithm due to D\k{a}browski and Plandowski. Then, using a couple of heuristics as well as more detailed time analysis the running time is lowered to O(n) in RAM model. Unfortunately no new properties of solutions are shown.Comment: submitted to a journal, general overhaul over the previous versio

Fast Label Extraction in the CDAWG

The compact directed acyclic word graph (CDAWG) of a string $T$ of length $n$ takes space proportional just to the number $e$ of right extensions of the maximal repeats of $T$, and it is thus an appealing index for highly repetitive datasets, like collections of genomes from similar species, in which $e$ grows significantly more slowly than $n$. We reduce from $O(m\log{\log{n}})$ to $O(m)$ the time needed to count the number of occurrences of a pattern of length $m$, using an existing data structure that takes an amount of space proportional to the size of the CDAWG. This implies a reduction from $O(m\log{\log{n}}+\mathtt{occ})$ to $O(m+\mathtt{occ})$ in the time needed to locate all the $\mathtt{occ}$ occurrences of the pattern. We also reduce from $O(k\log{\log{n}})$ to $O(k)$ the time needed to read the $k$ characters of the label of an edge of the suffix tree of $T$, and we reduce from $O(m\log{\log{n}})$ to $O(m)$ the time needed to compute the matching statistics between a query of length $m$ and $T$, using an existing representation of the suffix tree based on the CDAWG. All such improvements derive from extracting the label of a vertex or of an arc of the CDAWG using a straight-line program induced by the reversed CDAWG.Comment: 16 pages, 1 figure. In proceedings of the 24th International Symposium on String Processing and Information Retrieval (SPIRE 2017). arXiv admin note: text overlap with arXiv:1705.0864

Privacy Considerations when Designing Social Network Systems to Support Successful Ageing

A number of interventions exist to support older adults in ageing well and these typically involve support for an active and sociable ageing process. We set out to examine the privacy implications of an intervention that would monitor mobility and share lifestyle and health data with a community of trusted others. We took a privacy-by-design approach to the system in the early stages of its development, working with older adults to firstly understand their networks of trust and secondly understand their privacy concerns should information be exchanged across that network. We used a Johari Windows framework in the thematic analysis of our data, concluding that the social sharing of information in later life carried significant risk. Our participants worried about the social signaling associated with data sharing and were cautious about a system that had the potential to disrupt established networks

Challenges and Opportunities: What Can We Learn from Patients Living with Chronic Musculoskeletal Conditions, Health Professionals and Carers about the Concept of Health Literacy Using Qualitative Methods of Inquiry?

The field of health literacy continues to evolve and concern public health researchers and yet remains a largely overlooked concept elsewhere in the healthcare system. We conducted focus group discussions in England UK, about the concept of health literacy with older patients with chronic musculoskeletal conditions (mean age = 73.4 years), carers and health professionals. Our research posed methodological, intellectual and practical challenges. Gaps in conceptualisation and expectations were revealed, reiterating deficiencies in predominant models for understanding health literacy and methodological shortcomings of using focus groups in qualitative research for this topic. Building on this unique insight into what the concept of health literacy meant to participants, we present analysis of our findings on factors perceived to foster and inhibit health literacy and on the issue of responsibility in health literacy. Patients saw health literacy as a result of an inconsistent interactive process and the implications as wide ranging; healthcare professionals had more heterogeneous views. All focus group discussants agreed that health literacy most benefited from good inter-personal communication and partnership. By proposing a needs-based approach to health literacy we offer an alternative way of conceptualising health literacy to help improve the health of older people with chronic conditions