Sub-quadratic Time Complexity Research Articles

An independent condensed nearest neighbor classification technique for medical image retrieval

Nowadays, medical images play a vital role in the clinical diagnosis system, because these images contain a vast amount of medical information. The huge amount of medical images is generated everyday using the digital imaging techniques in medical examination centers and hospitals. The generated data are stored in large database and retrieving the same images is a significant task for better diagnosis. However, manual retrieval of clinical data is a tough and time consuming process due to the large database. The memory requirement and computation complexity of the existing condensed nearest neighbor (CNN) is more, it is solved by proposed independent condensed nearest neighbor (ICNN). The ICNN classification technique is developed to automatically retrieve the medical images from large database. The important features are extracted by using histogram of gradient (HOG) technique. The sub-quadratic time complexity presented in ICNN requires only few iterations to retrieve the query images, which improves the retrieval accuracy of the proposed technique. The experiments are used to test the performance of ICNN method in terms of classification and retrieval presentation. The proposed ICNN method outperforms existing CNN method by achieving specificity of 99.55% in the classification performance.

A Contrast Metric for Fraud Detection in Rich Graphs

How can we detect fraud in a big graph with rich properties, as online fraudsters invest more resources, including purchasing large pools of fake user accounts and dedicated IPs, to hide their fraudulent attacks? To achieve robustness, existing approaches detected dense sub-graphs as suspicious patterns in an unsupervised way, such as average degree maximization. However, such approaches suffer from the bias of including more nodes than necessary, resulting in lower accuracy and increased need for manual verification. Therefore, we propose HoloScope, which introduces a novel metric “contrast suspiciousness” integrating information from graph topology and spikes to more accurately detect fraudulent users and objects. Contrast suspiciousness dynamically emphasizes the contrasting patterns between fraudsters and normal users, making HoloScope capable of distinguishing the synchronized and strange behaviors of fraudsters by means of topology, bursts and drops, and rating scores. In addition, we provide theoretical bounds for how much this method increases the time cost needed for fraudsters to conduct adversarial attacks. Moreover, HoloScope has a concise framework and sub-quadratic time complexity, making the algorithm reproducible and scalable. In extensive experiments, HoloScope achieved significant accuracy improvements on real data with injected labels and true labels, when compared with state-of-the-art fraud detection methods.

PROMETHEE is not quadratic: An [formula omitted] algorithm

It is generally believed that the preference ranking method PROMETHEE has a quadratic time complexity. In this paper, however, we present an exact algorithm that computes PROMETHEE’s net flow scores in time O(qnlog(n)), where q represents the number of criteria and n the number of alternatives. The method is based on first sorting the alternatives after which the unicriterion flow scores of all alternatives can be computed in one scan over the sorted list of alternatives while maintaining a sliding window. This method works with the linear and level criterion preference functions. The algorithm we present is exact and, due to the sub-quadratic time complexity, vastly extends the applicability of the PROMETHEE method. Experiments show that with the new algorithm, PROMETHEE can scale up to millions of tuples.

Analytical Clustering Score with Application to Postplacement Register Clustering

Circuit clustering is usually done through discrete optimizations to enable circuit size reduction or design-specific cluster formation. In this article, we are interested in the register-clustering technique for clock-power reduction by leveraging new opportunities introduced by multibit flip-flop (MBFF). Currently, INTEGRA is the only existing postplacement MBFF clustering optimizer with a subquadratic time complexity. However, it severely degrades the wirelength, especially for realistic designs, which may nullify the benefits of MBFF clustering. In contrast, we formulate an analytical clustering score with a nonlinear programming framework, in which the wirelength objective can be seamlessly integrated and the solver has empirical subquadratic time complexity. With the MBFF library, the application of our analytical clustering method achieves comparable clock power to the state-of-the-art techniques, but further reduces the wirelength by about 25%. Even without the MBFF library, we can still achieve 30% clock wirelength reduction. In addition, the proposed method can potentially be integrated into an in-placement MBFF clustering solver and be applied to other problems that require formulating clustering scores in their objective functions.

Fast multi-sequence shift-register synthesis with the Euclidean algorithm

Feng and Tzeng's generalization of the Extended Euclidean Algorithmsynthesizes the shortest-length linear feedback shift-register for $s \geq 1$ sequences, where each sequence has the same length $n$. In this contribution, it is shown that Feng and Tzeng's algorithm which solves this multi-sequence shift-register problem has time complexity $\mathcal{O}(sn^2)$. An acceleration based on the Divide and Conquer strategy is proposed and it is proven that subquadratic time complexity is achieved.

Asymptotically efficient algorithms for skyline probabilities of uncertain data

Skyline computation is widely used in multicriteria decision making. As research in uncertain databases draws increasing attention, skyline queries with uncertain data have also been studied. Some earlier work focused on probabilistic skylines with a given threshold; Atallah and Qi [2009] studied the problem to compute skyline probabilities for all instances of uncertain objects without the use of thresholds, and proposed an algorithm with subquadratic time complexity. In this work, we propose a new algorithm for computing all skyline probabilities that is asymptotically faster: worst-case O(n √ n log n ) time and O(n) space for 2D data; O ( n 2−1/d log d −1 n ) time and O(n log d −2 n ) space for d -dimensional data. Furthermore, we study the online version of the problem: Given any query point p (unknown until the query time), return the probability that no instance in the given data set dominates p . We propose an algorithm for answering such an online query for d -dimensional data in O(n 1−1/ d log d −1 n ) time after preprocessing the data in O(n 2−1/d log d −1 ) time and space.

CarpeDiem: Optimizing the Viterbi Algorithm and Applications to Supervised Sequential Learning

The growth of information available to learning systems and the increasing complexity of learning tasks determine the need for devising algorithms that scale well with respect to all learning parameters. In the context of supervised sequential learning, the Viterbi algorithm plays a fundamental role, by allowing the evaluation of the best (most probable) sequence of labels with a time complexity linear in the number of time events, and quadratic in the number of labels. In this paper we propose CarpeDiem, a novel algorithm allowing the evaluation of the best possible sequence of labels with a sub-quadratic time complexity. We provide theoretical grounding together with solid empirical results supporting two chief facts. CarpeDiem always finds the optimal solution requiring, in most cases, only a small fraction of the time taken by the Viterbi algorithm; meantime, CarpeDiem is never asymptotically worse than the Viterbi algorithm, thus confirming it as a sound replacement.

On the Planar Piecewise Quadratic 1-Center Problem

In this paper we introduce a minimax model unifying several classes of single facility planar center location problems. We assume that the transportation costs of the demand points to the serving facility are convex functions {Q i }, i=1,…,n, of the planar distance used. Moreover, these functions, when properly transformed, give rise to piecewise quadratic functions of the coordinates of the facility location. In the continuous case, using results on LP-type models by Clarkson (J. ACM 42:488–499, 1995), Matousek et al. (Algorithmica 16:498–516, 1996), and the derandomization technique in Chazelle and Matousek (J. Algorithms 21:579–597, 1996), we claim that the model is solvable deterministically in linear time. We also show that in the separable case, one can get a direct O(nlog n) deterministic algorithm, based on Dyer (Proceedings of the 8th ACM Symposium on Computational Geometry, 1992), to find an optimal solution. In the discrete case, where the location of the center (server) is restricted to some prespecified finite set, we introduce deterministic subquadratic algorithms based on the general parametric approach of Megiddo (J. ACM 30:852–865, 1983), and on properties of upper envelopes of collections of quadratic arcs. We apply our methods to solve and improve the complexity of a number of other location problems in the literature, and solve some new models in linear or subquadratic time complexity.

Advances on sorting by reversals

The problem of sorting signed permutations by reversals is inspired by genome rearrangement problems in computational molecular biology. Given two genomes represented as signed permutations of the same elements (e.g. orthologous genes), the problem consists in finding a most parsimonious scenario of reversals that transforms one genome into the other. Following the first polynomial solution of this problem, several improvements, simplifications, generalizations, tutorials or surveys have been published on the subject. While the reversal distance problem—i.e. the problem of computing the minimum number of reversals in a sorting sequence, without giving the sequence itself—seems to be well explored, the problem of giving a scenario realizing the distance still raises some open questions, one of which by Ozery-Flato and Shamir about whether an algorithm with subquadratic time complexity could ever be achieved for solving the problem. We give a positive answer to this question by describing an algorithm of time complexity O ( n 3 / 2 log n ) .

Some (in)translatability results for normal logic programs and propositional theories

In this article, we compare the expressive powers of classes of normal logic programs that are obtained by constraining the number of positive subgoals (n) in the bodies of rules. The comparison is based on the existence/nonexistence of polynomial, faithful, and modular (PFM) translation functions between the classes. As a result, we obtain a strict ordering among the classes under consideration. Binary programs (n ⪯ 2) are shown to be as expressive as unconstrained programs but strictly more expressive than unary programs (n ⪯ 1) which, in turn, are strictly more expressive than atomic programs (n = 0). We also take propositional theories into consideration and prove them to be strictly less expressive than atomic programs. In spite of the gap in expressiveness, we develop a faithful but non-modular translation function from normal programs to propositional theories. We consider this as a breakthrough due to sub-quadratic time complexity (of the order of ||P|| × log2 |Hb(P)|). Furthermore, we present a prototype implementation of the translation function and demonstrate its promising performance with SAT solvers using three benchmark problems.