Dn Log Research Articles

An extension of the FFT‐based algorithm for the match‐count problem to weighted scores

The match‐count problem on strings is the basic problem of counting the matches of characters between two strings for every possible alignment. The problem is classically computed in O(σ n log m) time using a fast Fourier transform (FFT) for two strings of lengths m and n (m ≤ n) over an alphabet of size σ. This paper extends the target of this FFT‐based algorithm to a weighted version of the problem, which computes the sum of similarities between characters instead of the number of matches. The algorithm extended in this paper can solve the weighted match‐count problem in O(dn log m) time by mapping characters to numerical vectors of dimensionality d. This paper also evaluates the usefulness of the extended algorithm by applying it to plagiarism detection in documents. The experimental results show that the proposed algorithm is applicable to general vector representation of words and that the obtained plagiarism detection method can extremely reduce the processing time with a slight decrease of accuracy from the method based on the normal match‐count problem.

The prognostic value of high sensitivity cardiac troponin T in patients with congenital heart disease

BackgroundCardiac troponin T (cTnT) is a specific marker of myocardial injury that is elevated in patients with coronary artery disease or heart failure; it has been investigated as a prognostic marker. A highly sensitive, commercially available assay has been developed to detect cardiac troponin T (hs-cTnT). This study aimed to evaluate the clinical implications and prognostic value of hs-cTnT in patients with congenital heart disease (CHD). MethodsWe evaluated 122 consecutive patients hospitalized at our institution because of heart failure or scheduled cardiac catheterization. We measured the serum concentration of hs-cTnT at the time of hospitalization, and we prospectively followed-up all patients for 3 years and monitored rates of cardiovascular events (e.g. cardiac death, readmission owing to worsening of heart failure or arrhythmia, and reintervention) as endpoints. ResultsWe classified the patients according to their hs-cTnT level into non-detectable (ND group, hs-cTnT <0.003ng/mL), detectable normal (DN group, 0.003ng/mL ≤hs-cTnT <0.014ng/mL), or elevated (EL group, 0.014ng/mL ≤hs-cTnT) group; 20 of 122 (16.4%) patients were in the EL group, in which 17 cardiovascular events occurred during follow-up. In the multivariate Cox proportional hazard analyses, the EL group [p=0.024, hazard ratio (HR) 2.7, 95% confidence interval (CI) 1.1–5.8] was an independent significant predictor of cardiovascular events. A Kaplan–Meier curve revealed a high incidence of cardiovascular events in the EL group (EL vs ND log rank p<0.0001, HR 7.6, 95% CI 3.2–20.0, EL vs DN log rank p<0.0001, HR 4.1, 95% CI 2.1–7.8). ConclusionsBecause the EL group is more likely to have an adverse outcome, elevated hs-cTnT level can be a prognostic marker in patients with CHD.

The Boundary Forest Algorithm for Online Supervised and Unsupervised Learning

We describe a new instance-based learning algorithm called the Boundary Forest (BF) algorithm, that can be used for supervised and unsupervised learning. The al- gorithm builds a forest of trees whose nodes store previ- ously seen examples. It can be shown data points one at a time and updates itself incrementally, hence it is nat- urally online. Few instance-based algorithms have this property while being simultaneously fast, which the BF is. This is crucial for applications where one needs to respond to input data in real time. The number of chil- dren of each node is not set beforehand but obtained from the training procedure, which makes the algorithm very flexible with regards to what data manifolds it can learn. We test its generalization performance and speed on a range of benchmark datasets and detail in which settings it outperforms the state of the art. Empirically we find that training time scales as O(DN log(N )) and testing as O(Dlog(N)), where D is the dimensionality and N the amount of data.

Efficient Scheduling for Real-Time Pinwheel Tasks on DVS Processors

In this paper, we focus on the pinwheel task model for a variable voltage processor with d discrete voltage/speed levels. We propose an intra-task DVS algorithm which constructs a minimum energy schedule for k tasks in O(d+ k log k) time. Previous approaches solve this problem by generating a canonical schedule beforehand and adjusting the tasks' speed in O(dn log n) or O(n3) time. However, the length of a canonical schedule depends on the hyperperiod of those task periods and is of exponential length in general. In our approach, the tasks with arbitrary periods are first transformed into harmonic periods and then profile their key features. Afterward, an optimal discrete voltage schedule can be computed directly from those features.

An Efficient DVS Algorithm for Pinwheel Task Schedules

In this paper, we focus on the pinwheel task model with a variable voltage processor with d discrete voltage/speed levels. We propose an intra-task DVS algorithm, which constructs a minimum energy schedule for k tasks in O(d+k log k) time We also give an inter-task DVS algorithm with O(d+n log n) time, where n denotes the number of jobs. Previous approaches solve this problem by generating a canonical schedule beforehand and adjusting the tasks' speed in O(dn log n) or O(<TEX>$n^3$</TEX>) time. However, the length of a canonical schedule depends on the hyper period of those task periods and is of exponential length in general. In our approach, the tasks with arbitrary periods are first transformed into harmonic periods and then profile their key features. Afterward, an optimal discrete voltage schedule can be computed directly from those features.

Efficient voting prediction for pairwise multilabel classification

The pairwise approach to multilabel classification reduces the problem to learning and aggregating preference predictions among the possible labels. A key problem is the need to query a quadratic number of preferences for making a prediction. To solve this problem, we extend the recently proposed QWeighted algorithm for efficient pairwise multiclass voting to the multilabel setting, and evaluate the adapted algorithm on several real-world datasets. We achieve an average-case reduction of classifier evaluations from n 2 to n + dn log n , where n is the total number of possible labels and d is the average number of labels per instance, which is typically quite small in real-world datasets.

Deterministic Broadcast and Gossiping Algorithms for Ad hoc Networks

We present in this paper three deterministic broadcast and a gossiping algorithm suitable for ad hoc networks where topology changes range from infrequent to very frequent. The proposed algorithms are designed to work in networks where the mobile nodes possessing collision detection capabilities. Our first broadcast algorithm accomplishes broadcast in O(nlog n) for networks where topology changes are infrequent. We also present an O(nlog n) worst case time broadcast algorithms that is resilient to mobility. For networks where topology changes are frequent, we present a third algorithm that accomplishes broadcast in O(?·nlog n + n·|M|) in the worst case scenario, where |M| is the length of the message to be broadcasted and ? the maximum node degree. We then extend one of our broadcast algorithms to develop an O(Dn log n + D2) algorithm for gossiping in the same network model.

Attribute value reordering for efficient hybrid OLAP

The normalization of a data cube is the ordering of the attribute values. For large multidimensional arrays where dense and sparse chunks are stored differently, proper normalization can lead to improved storage efficiency. We show that it is NP-hard to compute an optimal normalization even for 1 × 3 chunks, although we find an exact algorithm for 1 × 2 chunks. When dimensions are nearly statistically independent, we show that dimension-wise attribute frequency sorting is an optimal normalization and takes time O( dn log( n)) for data cubes of size n d . When dimensions are not independent, we propose and evaluate a several heuristics. The hybrid OLAP (HOLAP) storage mechanism is already 19–30% more efficient than ROLAP, but normalization can improve it further by 9–13% for a total gain of 29–44% over ROLAP.

Deformation theory and the computation of zeta functions

We present a new approach to the problem of computing the zeta function of a hypersurface over a finite field. For a hypersurface defined by a polynomial of degree d in n variables over the field of q elements, one desires an algorithm whose running time is a polynomial function of dn log(q). (Here we assume d ⩾ 2, for otherwise the problem is easy.) The case n = 1 is related to univariate polynomial factorisation and is comparatively straightforward. When n = 2 one is counting points on curves, and the method of Schoof and Pila yields a complexity of log ⁡ ( q ) C d , where the function Cd depends exponentially on d. For arbitrary n, the theorem of the author and Wan gives a complexity which is a polynomial function of (pdn log(q))n, where p is the characteristic of the field. A complexity estimate of this form can also be achieved for smooth hypersurfaces using the method of Kedlaya, although this has only been worked out in full for curves. The new approach we present should yield a complexity which is a small polynomial function of pdn log(q). In this paper, we work this out in full for Artin–Schreier hypersurfaces defined by equations of the form Zp − Z = f, where the polynomial f has a diagonal leading form. The method utilises a relative p-adic cohomology theory for families of hypersurfaces, due in essence to Dwork. As a corollary of our main theorem, we obtain the following curious result. Let f be a multivariate polynomial with integer coefficients whose leading form is diagonal. There exists an explicit deterministic algorithm which takes as input a prime p, outputs the number of solutions to the congruence equation f = 0 op, and runs in {\mathcal O}(p^{2 + \varepsilon}) bit operations, for any ε > 0. This improves upon the elementary estimate of {\mathcal O}(p^{n-1 + \varepsilon}) bit operations, where n is the number of variables, which can be achieved using Berlekamp's root counting algorithm. 2000 Mathematics Subject Classification 11Y99, 11M38, 11T99.

Fast stabbing of boxes in high dimensions

We present in this paper a simple yet efficient algorithm for stabbing a set S of n axis-parallel boxes in d-dimensional space with c( S) points in output-sensitive time O(dn log c( S)) and linear space. Let c ∗( S) and b ∗( S) be, respectively, the minimum number of points required to stab S and the maximum number of pairwise disjoint boxes of S . We prove that b ∗( S)⩽c ∗( S)⩽c( S)⩽b ∗( S)(1+ log 2 b ∗( S)) d−1 . Since finding a minimal set of c ∗( S) points is NP-complete as soon as d>1, we obtain a fast precision-sensitive heuristic for stabbing S whose quality does not depend on the input size. In the case of congruent or constrained isothetic boxes, our algorithm reports, respectively, c( S)⩽2 d−1b ∗( S) and c( S)=O d(b ∗( S)) stabbing points. Moreover, we show that the bounds we get on c( S) are asymptotically tight and corroborate our results with some experiments. We also describe an optimal output-sensitive algorithm for finding a minimal-size optimal stabbing point-set of intervals. Finally, we conclude with insights for further research.

AN EFFICIENT DIVIDE-AND-CONQUER APPROXIMATION ALGORITHM FOR PARTITIONING INTO D-BOXES

Let P be a set of n points located inside a d-box (rectangle if d=2) R. We study the problem of partitioning R into d-boxes by introducing a set of hyperplane (line if d=2) segments of least total (d-1)–volume (length if d=2). Each of the resulting d-boxes in a valid partition cannot contain points from P as interior points. Since this problem is computationally intractable (NP-hard) even when d=2, we present an efficient approximation algorithm for its solution. The partition generated by our approximation algorithm is guaranteed to be within 2d times the optimal solution value. We also present a problem instance for each d≥2 for which the approximation bound is tight for the algorithm. The time complexity for our algorithm is O(dn log n).

Approximate closest-point queries in high dimensions

Given n points in d dimensions, we show how to construct a data structure of space O( d2 d n) that approximately answers closest-point queries in time O( d2 d log n). The returned point is at most O(d> 1 2 ) times further from the query point than the true closest point. We also show how to construct a data structure of space O( dn log m), that—with high probability—can answer a sequence of m closest-point queries in time O( d log n log m) per query, with approximation ratio O(d 3 2 ) . Our data structures are based on quadtrees.