We consider the problem of finding inscribed boxes and axis-aligned inscribed boxes of maximum volume, inside a compact and solid convex set. Our algorithms are capable of solving these two problems in any such set that can be represented with finite number of convex inequalities. For the axis-aligned case, we formulate the problem for higher dimensions and present an exact optimization algorithm which solves the problem in @math time, where @math is the dimension and @math is the number of inequalities defining the convex set. For the general case, after formulating the problem for higher dimensions we investigate the traditional 2-dimensional problem, which is in the literature merely considered for convex polygons, for a broad range of convex sets. We first present a new exact algorithm that finds the largest inscribed axis-aligned rectangle in such convex sets for any given direction of axes in @math time. Using this exact algorithm as a subroutine, we present an @math -approximation algorithm that computes @math -approximation to the largest inscribed rectangle with computational complexity of @math . Finally, we show that how this running time can be improved to @math with a @math pre-processing time when the convex set is a polygon.
To our knowledge, except Amenta's model @cite_28 for LIAR and the model of @cite_22 for LIR, no other optimization based algorithm published so far for these two problems. Again, except Amenta's model for LIAR @cite_28 , we are not aware of any model or algorithm for the higher dimension problem. Our optimization model for LIAR is much more efficient than Amenta's model. Also none of the algorithms in the literature are able to solve both problems, while our parametric approach is able to do so in 2-dimensional case. Moreover, except 's algorithm @cite_22 , no algorithm is published so far for either of these problems that is capable of dealing with other geometric convex sets such as ellipses and not just polygons. In 's algorithm @cite_22 it is not clear whether those two queries are doable for any convex set and if yes what would @math be in their algorithm's running time. Our algorithm is unique in the sense that its performance depends to the number of inequalities defining a convex set, e.g. while for a polygon this is @math for an ellipse this is one.
@cite_28 @cite_22
2048733643 1688647404
We investigate the minimization of Newton's functional for the problem of the body of minimal resistance with maximal height @math cite butt in the class of convex developable functions defined in a disc. This class is a natural candidate to find a (non-radial) minimizer in accordance with the results of cite lrp2. We prove that the minimizer in this class has a minimal set in the form of a regular polygon with @math sides centered in the disc, and numerical experiments indicate that the natural number @math is a non-decreasing function of @math . The corresponding functions all achieve a lower value of the functional than the optimal radially symmetric function with the same height @math . A set L@?V(G) of a graph G=(V,E) is a liar's dominating set if (1) for all v@?V(G), |N"G[v]@?L|>=2 and (2) for every pair u,v@?V(G) of distinct vertices, |(N"G[u]@?N"G[v])@?L|>=3. A graph G=(V,E) admits a liar's dominating set if each of its connected component has at least three vertices. Given a graph G=(V,E) and an integer K, the liar's domination decision problem (LR-DOMDP) is to decide whether G has a liar's dominating set of cardinality at most K. Slater [P.J. Slater, Liar's Domination, Networks, 54(2) (2009) 70-74] proved that the LR-DOMDP is NP-complete for general graphs. Subsequently, Roden and Slater [M.L. Roden and P.J. Slater, Liar's domination in graphs, Discrete Math., 309(19) (2009) 5884-5890] showed a more general family of problems to each be NP-complete for bipartite graphs. Besides this result, no other algorithmic result for the liar's dominating set problem is available in the literature. In this paper, we first strengthen the complexity result of the LR-DOMDP by showing that this problem remains NP-complete for split graphs and hence for chordal graphs. Finally, we propose a linear time algorithm for computing a minimum cardinality liar's dominating set in a tree. We study a class of optimization problems in polygons that seek to compute the "largest" subset of a prescribed type, e.g., a longest line segment ("stick") or a maximum-area triangle or convex body ("potato"). Exact polynomial-time algorithms are known for some of these problems, but their time bounds are high (e.g., O(n7) for the largest convex polygon in a simple n-gon). We devise efficient approximation algorithms for these problems. In particular, we give near-linear time algorithms for a (1 - ∈)-approximation of the biggest stick, an O(1)-approximation of the maximum-area convex body, and a (1 - ∈)-approximation of the maximum-area fat triangle or rectangle. In addition, we give efficient methods for computing large ellipses inside a polygon (whose vertices are a dense sampling of a closed smooth curve). Our algorithms include both deterministic and randomized methods, one of which has been implemented (for computing large area ellipses in a well sampled closed smooth curve). Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . A subset L ? V of a graph G = ( V , E ) is called a liar's dominating set of G if (i) | N G u ] ? L | ? 2 for every vertex u ? V , and (ii) | ( N G u ] ? N G v ] ) ? L | ? 3 for every pair of distinct vertices u , v ? V . The Min Liar Dom Set problem is to find a liar's dominating set of minimum cardinality of a given graph G and the Decide Liar Dom Set problem is the decision version of the Min Liar Dom Set problem. The Decide Liar Dom Set problem is known to be NP-complete for general graphs. In this paper, we first present approximation algorithms and hardness of approximation results of the Min Liar Dom Set problem in general graphs, bounded degree graphs, and p-claw free graphs. We then show that the Decide Liar Dom Set problem is NP-complete for doubly chordal graphs and propose a linear time algorithm for computing a minimum liar's dominating set in block graphs. We propose a novel geometric structure induced by any given convex polygon @math , called @math , which is an arrangement of @math segments, each of which is parallel to an edge of @math , where @math denotes the number of edges of @math . This structure enjoys six simple yet nontrivial properties, which can be derived from two elementary geometric properties -- convexity and parallelism. We then apply @math to solve the geometric optimization problem of computing the parallelogram(s) in @math with the maximum area. We show that the essential nature of the locally maximal area parallelograms is captured by @math and that computing all these parallelograms reduces to answering @math location queries on @math . We answer each of these queries in @math time, and thus obtain an @math time algorithm for this optimization problem. Our algorithm avoids an explicit construction of @math , which would take @math time. In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] Convex and submodular functions play an important role in many applications, and in particular in combinatorial optimization. Here we study two special cases: convexity in one dimension and submodularity in two dimensions. The latter type of functions are equivalent to the well-known Monge matrices. A matrix @math is called a Monge matrix if for every @math and @math we have @math . If inequality holds in the opposite direction, then V is an inverse Monge matrix (supermodular function). Many problems, such as the traveling salesperson problem and various transportation problems, can be solved more efficiently if the input is a Monge matrix. In this work we present testing algorithms for the above properties. A testing algorithm for a predetermined property @math is given query access to an unknown function f and a distance parameter @math . The algorithm should accept f with high probability if it has the property @math and reject it with high probability if more than an @math -fraction of the function values should be modified so that f obtains the property. Our algorithm for testing whether a 1-dimensional function @math is convex (concave) has query complexity and running time of @math . Our algorithm for testing whether an n1 × n2 matrix V is a Monge (inverse Monge) matrix has query complexity and running time of @math . We revisit the following problem: Given a convex polygon @math , find the largest-area inscribed triangle. We show by example that the linear-time algorithm presented in 1979 by Dobkin and Snyder for solving this problem fails. We then proceed to show that with a small adaptation, their approach does lead to a quadratic-time algorithm. We also present a more involved @math time divide-and-conquer algorithm. Also we show by example that the algorithm presented in 1979 by Dobkin and Snyder for finding the largest-area @math -gon that is inscribed in a convex polygon fails to find the optimal solution for @math . Finally, we discuss the implications of our discoveries on the literature. We consider the problem of finding the maximum area parallelogram (MAP) inside a given convex polygon. Our main result is an algorithm for computing the MAP in an @math -sided polygon in @math time. Achieving this running time requires proving several new structural properties of the MAP. Our algorithm actually computes all the locally maximal area parallelograms (LMAPs). In addition to the algorithm, we prove that the LMAPs interleave each other, thus the number of LMAPs is bounded by @math . We discuss applications of our result to, among others, the problem of computing the maximum area centrally-symmetric convex body (MAC) inside a convex polygon, and the simplest case of the Heilbronn Triangle Problem. Let G=(V,E) be a graph without isolated vertices and having at least 3 vertices. A set L@?V(G) is a liar@?s dominating set if (1) |N"G[v]@?L|>=2 for all v@?V(G), and (2) |(N"G[u]@?N"G[v])@?L|>=3 for every pair u,v@?V(G) of distinct vertices in G, where N"G[x]= y@?V|xy@?E @? x is the closed neighborhood of x in G. Given a graph G and a positive integer k, the liar@?s domination problem is to check whether G has a liar@?s dominating set of size at most k. The liar@?s domination problem is known to be NP-complete for general graphs. In this paper, we propose a linear time algorithm for computing a minimum cardinality liar@?s dominating set in a proper interval graph. We also strengthen the NP-completeness result of liar@?s domination problem for general graphs by proving that the problem remains NP-complete even for undirected path graphs which is a super class of proper interval graphs. Let S be a set of n points in the Euclidean plane. The convex layers of S are the convex polygons obtained by iterating on the following procedure: compute the convex hull of S and remove its vertices from S . This process of peeling a planar point set is central in the study of robust estimators in statistics. It also provides valuable information on the morphology of a set of sites and has proven to be an efficient preconditioning for range search problems. An optimal algorithm is described for computing the convex layers of S. The algorithm runs in 0 (n n) time and requires O(n) space. Also addressed is the problem of determining the depth of a query point within the convex layers of S , i.e., the number of layers that enclose the query point. This is essentially a planar point location problem, for which optimal solutions are therefore known. Taking advantage of structural properties of the problem, however, a much simpler optimal solution is derived. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Inner approximation algorithms have had two major roles in the mathematical programming literature. Their first role was in the construction of algorithms for the decomposition of large-scale mathematical programs, such as in the Dantzig-Wolfe decomposition principle. However, recently they have been used in the creation of algorithms that locate Kuhn-Tucker solutions to nonconvex programs. Avriel and Williams' Avriel, M., A. C. Williams. 1970. Complementary geometric programming. SIAM J. Appl. Math.19 125-141. complementary geometric programming algorithm, Duffin and Peterson's Duffin, R. J., E. L. Peterson. 1972. Reversed geometric programs treated by harmonic means. Indiana Univ. Math. J.22 531-550. reversed geometric programming algorithms, Reklaitis and Wilde's Reklaitis, G. V., D. J. Wilde. 1974. Geometric programming via a primal auxiliary problem. AIIE Trans.6 308-317. primal reversed geometric programming algorithm, and Bitran and Novaes' Bitran, G. R., A. G. Novaes. 1973. Linear programming with a fractional objective function. Opns. Res.21 22-29. linear fractional programming algorithm are all examples of this class of inner approximation algorithms. A sequence of approximating convex programs are solved in each of these algorithms. Rosen's Rosen, J. B. 1966. Iterative solution of nonlinear optimal control problems. SIAM J. Control4 223-244. inner approximation algorithm is a special case of the general inner approximation algorithm presented in this note. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. In this paper we analyze the randomized block-coordinate descent (RBCD) methods proposed in Nesterov (SIAM J Optim 22(2):341---362, 2012), Richtarik and Takaă? (Math Program 144(1---2):1---38, 2014) for minimizing the sum of a smooth convex function and a block-separable convex function, and derive improved bounds on their convergence rates. In particular, we extend Nesterov's technique developed in Nesterov (SIAM J Optim 22(2):341---362, 2012) for analyzing the RBCD method for minimizing a smooth convex function over a block-separable closed convex set to the aforementioned more general problem and obtain a sharper expected-value type of convergence rate than the one implied in Richtarik and Takaă? (Math Program 144(1---2):1---38, 2014). As a result, we also obtain a better high-probability type of iteration complexity. In addition, for unconstrained smooth convex minimization, we develop a new technique called randomized estimate sequence to analyze the accelerated RBCD method proposed by Nesterov (SIAM J Optim 22(2):341---362, 2012) and establish a sharper expected-value type of convergence rate than the one given in Nesterov (SIAM J Optim 22(2):341---362, 2012). In this paper we study new stochastic approximation (SA) type algorithms, namely, the accelerated SA (AC-SA), for solving strongly convex stochastic composite optimization (SCO) problems. Specifically, by introducing a domain shrinking procedure, we significantly improve the large-deviation results associated with the convergence rate of a nearly optimal AC-SA algorithm presented by Ghadimi and Lan in [SIAM J. Optim., 22 (2012), pp 1469--1492]. Moreover, we introduce a multistage AC-SA algorithm, which possesses an optimal rate of convergence for solving strongly convex SCO problems in terms of the dependence on not only the target accuracy, but also a number of problem parameters and the selection of initial points. To the best of our knowledge, this is the first time that such an optimal method has been presented in the literature. From our computational results, these AC-SA algorithms can substantially outperform the classical SA and some other SA type algorithms for solving certain classes of strongly... Classification, which involves finding rules that partition a given da.ta set into disjoint groups, is one class of data mining problems. Approaches proposed so far for mining classification rules for large databases are mainly decision tree based symbolic learning methods. The connectionist approach based on neura.l networks has been thought not well suited for data mining. One of the major reasons cited is that knowledge generated by neural networks is not explicitly represented in the form of rules suitable for verification or interpretation by humans. This paper examines this issue. With our newly developed algorithms, rules which are similar to, or more concise than those generated by the symbolic methods can be extracted from the neural networks. The data mining process using neural networks with the emphasis on rule extraction is described. ExperimenM results and comparison with previously published works are presented.