A Comparative Analysis of the Performance of Alternative Stock Valuation Ratios Using Stochastic Dominance with a Riskless Asset

John R. Erickson is an Associate Professor of Finance in the Department of Finance, School of Business Administration and Economics, California State University, Fullerton. Albert J. Fredman is Professor of Finance in the Department of Finance, School of Business Administration and Economics, California State University, Fullerton

Augmenting graphs to minimize the diameter

We study the problem of augmenting a weighted graph by inserting edges of bounded total cost while minimizing the diameter of the augmented graph. Our main result is an FPT 4-approximation algorithm for the problem.Comment: 15 pages, 3 figure

Dynamic Range Majority Data Structures

Given a set $P$ of coloured points on the real line, we study the problem of answering range $\alpha$-majority (or "heavy hitter") queries on $P$. More specifically, for a query range $Q$, we want to return each colour that is assigned to more than an $\alpha$-fraction of the points contained in $Q$. We present a new data structure for answering range $\alpha$-majority queries on a dynamic set of points, where $\alpha \in (0,1)$. Our data structure uses O(n) space, supports queries in $O((\lg n) / \alpha)$ time, and updates in $O((\lg n) / \alpha)$ amortized time. If the coordinates of the points are integers, then the query time can be improved to $O(\lg n / (\alpha \lg \lg n) + (\lg(1/\alpha))/\alpha))$. For constant values of $\alpha$, this improved query time matches an existing lower bound, for any data structure with polylogarithmic update time. We also generalize our data structure to handle sets of points in d-dimensions, for $d \ge 2$, as well as dynamic arrays, in which each entry is a colour.Comment: 16 pages, Preliminary version appeared in ISAAC 201

Faster algorithms for 1-mappability of a sequence

In the k-mappability problem, we are given a string x of length n and integers m and k, and we are asked to count, for each length-m factor y of x, the number of other factors of length m of x that are at Hamming distance at most k from y. We focus here on the version of the problem where k = 1. The fastest known algorithm for k = 1 requires time O(mn log n/ log log n) and space O(n). We present two algorithms that require worst-case time O(mn) and O(n log^2 n), respectively, and space O(n), thus greatly improving the state of the art. Moreover, we present an algorithm that requires average-case time and space O(n) for integer alphabets if m = {\Omega}(log n/ log {\sigma}), where {\sigma} is the alphabet size

Caregiving, Metabolic Syndrome Indicators, and 1-year Decline in Walking Speed: Results of Caregiver-SOF

BACKGROUND Chronic stress may lead to health decline through metabolic syndrome. Thus, persons in stressful caregiving situations who also have more indicators of metabolic syndrome may experience more decline than other caregivers or noncaregivers. METHODS The sample included 921 women (338 caregivers and 583 noncaregivers) from the Caregiver-Study of Osteoporotic Fractures study. Participants had home-based baseline and 1-year follow-up interviews between 1999 and 2003. At baseline, caregivers were categorized as long term (³4 years) versus short term (<4 years), and caring for someone with Alzheimer's disease/dementia or not. A metabolic risk composite score was the sum of four indicators: body mass index ³30, and diagnosis or using medications for hypertension, diabetes, or high cholesterol. Walking speed (m/second) was measured at both interviews. RESULTS Walking speed declined for the total sample (adjusted mean = −0.005 m/second, ±0.16) over an average of 1.04 years (±0.16). Overall, caregiving was not associated with decline. Increasing metabolic risk score was associated with greater decline for the total sample and long-term and dementia caregivers, but not other caregivers or noncaregivers. Metabolic risk score modified the adjusted associations between years of caregiving and dementia caregiving with walking speed decline (p values for interaction terms were 0.039 and 0.057, respectively). The biggest declines were in long-term caregivers and dementia caregivers who also had 3–4 metabolic indicators (−0.10 m/second and −0.155 m/second, respectively). CONCLUSIONS Walking speed declined the most among older women who had both stressful caregiving situations and more metabolic syndrome indicators, suggesting these caregiver subgroups may have increased risk of health decline.AG18037, AG05407, AR35582, AG05394, AR35584, and AR3558

Bringing Order to Special Cases of Klee's Measure Problem

Klee's Measure Problem (KMP) asks for the volume of the union of n axis-aligned boxes in d-space. Omitting logarithmic factors, the best algorithm has runtime O*(n^{d/2}) [Overmars,Yap'91]. There are faster algorithms known for several special cases: Cube-KMP (where all boxes are cubes), Unitcube-KMP (where all boxes are cubes of equal side length), Hypervolume (where all boxes share a vertex), and k-Grounded (where the projection onto the first k dimensions is a Hypervolume instance). In this paper we bring some order to these special cases by providing reductions among them. In addition to the trivial inclusions, we establish Hypervolume as the easiest of these special cases, and show that the runtimes of Unitcube-KMP and Cube-KMP are polynomially related. More importantly, we show that any algorithm for one of the special cases with runtime T(n,d) implies an algorithm for the general case with runtime T(n,2d), yielding the first non-trivial relation between KMP and its special cases. This allows to transfer W[1]-hardness of KMP to all special cases, proving that no n^{o(d)} algorithm exists for any of the special cases under reasonable complexity theoretic assumptions. Furthermore, assuming that there is no improved algorithm for the general case of KMP (no algorithm with runtime O(n^{d/2 - eps})) this reduction shows that there is no algorithm with runtime O(n^{floor(d/2)/2 - eps}) for any of the special cases. Under the same assumption we show a tight lower bound for a recent algorithm for 2-Grounded [Yildiz,Suri'12].Comment: 17 page

On dualization in products of forests, in

Abstract. Let P = P1 ×...×Pn be the product of n partially ordered sets, each with an acyclic precedence graph in which either the in-degree or the out-degree of each element is bounded. Given a subset A⊆P,it is shown that the set of maximal independent elements of A in P can be incrementally generated in quasi-polynomial time. We discuss some applications in data mining related to this dualization problem

Compressed Subsequence Matching and Packed Tree Coloring

We present a new algorithm for subsequence matching in grammar compressed strings. Given a grammar of size $n$ compressing a string of size $N$ and a pattern string of size $m$ over an alphabet of size $\sigma$, our algorithm uses $O(n+\frac{n\sigma}{w})$ space and $O(n+\frac{n\sigma}{w}+m\log N\log w\cdot occ)$ or $O(n+\frac{n\sigma}{w}\log w+m\log N\cdot occ)$ time. Here $w$ is the word size and $occ$ is the number of occurrences of the pattern. Our algorithm uses less space than previous algorithms and is also faster for $occ=o(\frac{n}{\log N})$ occurrences. The algorithm uses a new data structure that allows us to efficiently find the next occurrence of a given character after a given position in a compressed string. This data structure in turn is based on a new data structure for the tree color problem, where the node colors are packed in bit strings.Comment: To appear at CPM '1

Computing discriminating and generic words

International audienceWe study the following three problems of computing generic or discriminating words for a given collection of documents. Given a pattern P and a threshold d, we want to report (i) all longest extensions of P which occur in at least d documents, (ii) all shortest extensions of P which occur in less than d documents, and (iii) all shortest extensions of P which occur only in d selected documents. For these problems, we propose efficient algorithms based on suffix trees and using advanced data structure techniques. For problem (i), we propose an optimal solution with constant running time per output word

Maximum Cliques in Protein Structure Comparison

Computing the similarity between two protein structures is a crucial task in molecular biology, and has been extensively investigated. Many protein structure comparison methods can be modeled as maximum clique problems in specific k-partite graphs, referred here as alignment graphs. In this paper, we propose a new protein structure comparison method based on internal distances (DAST) which is posed as a maximum clique problem in an alignment graph. We also design an algorithm (ACF) for solving such maximum clique problems. ACF is first applied in the context of VAST, a software largely used in the National Center for Biotechnology Information, and then in the context of DAST. The obtained results on real protein alignment instances show that our algorithm is more than 37000 times faster than the original VAST clique solver which is based on Bron & Kerbosch algorithm. We furthermore compare ACF with one of the fastest clique finder, recently conceived by Ostergard. On a popular benchmark (the Skolnick set) we observe that ACF is about 20 times faster in average than the Ostergard's algorithm