25 research outputs found

    The Non-Uniform k-Center Problem

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    In this paper, we introduce and study the Non-Uniform k-Center problem (NUkC). Given a finite metric space (X,d)(X,d) and a collection of balls of radii {r1rk}\{r_1\geq \cdots \ge r_k\}, the NUkC problem is to find a placement of their centers on the metric space and find the minimum dilation α\alpha, such that the union of balls of radius αri\alpha\cdot r_i around the iith center covers all the points in XX. This problem naturally arises as a min-max vehicle routing problem with fleets of different speeds. The NUkC problem generalizes the classic kk-center problem when all the kk radii are the same (which can be assumed to be 11 after scaling). It also generalizes the kk-center with outliers (kCwO) problem when there are kk balls of radius 11 and \ell balls of radius 00. There are 22-approximation and 33-approximation algorithms known for these problems respectively; the former is best possible unless P=NP and the latter remains unimproved for 15 years. We first observe that no O(1)O(1)-approximation is to the optimal dilation is possible unless P=NP, implying that the NUkC problem is more non-trivial than the above two problems. Our main algorithmic result is an (O(1),O(1))(O(1),O(1))-bi-criteria approximation result: we give an O(1)O(1)-approximation to the optimal dilation, however, we may open Θ(1)\Theta(1) centers of each radii. Our techniques also allow us to prove a simple (uni-criteria), optimal 22-approximation to the kCwO problem improving upon the long-standing 33-factor. Our main technical contribution is a connection between the NUkC problem and the so-called firefighter problems on trees which have been studied recently in the TCS community.Comment: Adjusted the figur

    Finding Even Subgraphs Even Faster

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    Problems of the following kind have been the focus of much recent research in the realm of parameterized complexity: Given an input graph (digraph) on nn vertices and a positive integer parameter kk, find if there exist kk edges (arcs) whose deletion results in a graph that satisfies some specified parity constraints. In particular, when the objective is to obtain a connected graph in which all the vertices have even degrees---where the resulting graph is \emph{Eulerian}---the problem is called Undirected Eulerian Edge Deletion. The corresponding problem in digraphs where the resulting graph should be strongly connected and every vertex should have the same in-degree as its out-degree is called Directed Eulerian Edge Deletion. Cygan et al. [\emph{Algorithmica, 2014}] showed that these problems are fixed parameter tractable (FPT), and gave algorithms with the running time 2O(klogk)nO(1)2^{O(k \log k)}n^{O(1)}. They also asked, as an open problem, whether there exist FPT algorithms which solve these problems in time 2O(k)nO(1)2^{O(k)}n^{O(1)}. In this paper we answer their question in the affirmative: using the technique of computing \emph{representative families of co-graphic matroids} we design algorithms which solve these problems in time 2O(k)nO(1)2^{O(k)}n^{O(1)}. The crucial insight we bring to these problems is to view the solution as an independent set of a co-graphic matroid. We believe that this view-point/approach will be useful in other problems where one of the constraints that need to be satisfied is that of connectivity

    Evaluation of Particulate Matter Pollution in Micro-Environments of Office Buildings—A Case Study of Delhi, India

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    High level of particulate matter in an office building is one of the prime concerns for occupant’s health and their work performance. The present study focuses on the evaluation of the distribution pattern of airborne particles in three office buildings in Delhi City. The study includes the Assessment of PM10, PM2.5 and PM1 in the different indoor environments, their particle size distribution, I/O ratio, a correlation between pollutants their sources and management practices. The features of buildings I, II, and III are old infrastructure, new modern infrastructure, and an old building with good maintenance. The results indicate that the average concentrations of PM10, PM2.5, and PM1 are found in the range of 55–150 μg m−3, 41–104 μg m−3 and 37–95 μg m−3, respectively in Building I, 33–136 μg m−3, 30–84 μg m−3 and 28–73 μg m−3, respectively in Building II and 216–330 μg m−3, 188–268 μg m−3 and 171–237 μg m−3, respectively in Building III. The maximum proportion of the total mass contributed by PM0.25–1.0 i.e., up to 75%, 86%, and 76% in the meeting room of Building I, II and III, respectively. The proportion of ultrafine particles was found higher in the office area where the movement was minimum and vice versa. The higher I/O indicates the contribution of the presence of indoor sources for ultra-fine and finer particles. Further, possible strategies for indoor air pollution control are also discussed

    ANALISIS SISTEM PENGGAJIAN PADA PMI CABANG SURAKARTA

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    We investigate the parameterized complexity of the following edge coloring problem motivated by the problem of channel assignment in wireless networks. For an integer q >= 2 and a graph G, the goal is to find a coloring of the edges of G with the maximum number of colors such that every vertex of the graph sees at most q colors. This problem is NP-hard for q >= 2, and has been well-studied from the point of view of approximation. Our main focus is the case when q = 2, which is already theoretically intricate and practically relevant. We show fixed-parameter tractable algorithms for both the standard and the dual parameter, and for the latter problem, the result is based on a linear vertex kernel

    Improved Approaches and Various study on image Steganography

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    Steganography is the sciences that include impart secretive information in an appropriate interactive media bearer, for eg, picture, sound, and video records. It comes beneath the assumption so as to if feature is visible, point of assault is obvious, thus aim here is for all time to hide the extremely existence of embedded data. Steganography has a variety of use applications. Though, like any other science it is able to use for the ill intentions. It has been impelled to front of present security strategies by momentous improvement in computational power, increment in wellbeing mindfulness by, e.g., individuals, groups, agency, and government and all the way through intellectual detection. A wide range of transporter record organizations can be utilized, yet advanced pictures are the most famous in view of their recurrence on the web. This paper presents two new procedures where in cryptography and steganography are united to scramble the data and notwithstanding cover the data in another medium through IP. This Report securing the picture by encryption is finished by DES calculation utilizing the key picture. The scrambled picture can be covering up in another picture by utilizing RSA procedures, with the goal that the mystery’s exceptionally presence is hidden. The decoding should be possible by a similar key picture utilizing DES calculation.

    UNO Gets Easier for a Single Player

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    This work is a follow up to 2, FUN 2010], which initiated a detailed analysis of the popular game of UNO (R). We consider the solitaire version of the game, which was shown to be NP-complete. In 2], the authors also demonstrate a (O)(n)(c(2)) algorithm, where c is the number of colors across all the cards, which implies, in particular that the problem is polynomial time when the number of colors is a constant. In this work, we propose a kernelization algorithm, a consequence of which is that the problem is fixed-parameter tractable when the number of colors is treated as a parameter. This removes the exponential dependence on c and answers the question stated in 2] in the affirmative. We also introduce a natural and possibly more challenging version of UNO that we call ``All Or None UNO''. For this variant, we prove that even the single-player version is NP-complete, and we show a single-exponential FPT algorithm, along with a cubic kernel

    Faster Deterministic Algorithms for r-Dimensional Matching Using Representative Sets

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    Given a universe U: = U1⊎ · · ·⊎Ur, and a r-uniform family F ⊆ U1× · · ·×Ur, the r-dimensional matching problem asks if F admits a collection of k mutually disjoint sets. The special case when r = 3 is the classic 3D-Matching problem. Recently, several improvements have been suggested for these (and closely related) problems in the setting of randomized parameterized algorithms. Also, many approaches have evolved for deterministic parameterized algorithms. For instance, for the 3D-Matching problem, a combination of color coding and iterative expansion yields a running time of O ∗ (2.80 (3k)), and for the r-dimensional matching problem, a recently developed derandomization for known algebraic techniques leads to a running time of O ∗ (5.44 (r−1)k). In this work, we employ techniques based on dynamic programming and representative families, leading to a deterministic algorithm with running time O ∗ (2.85 (r−1)k) for the r-Dimensional Matching problem. Further, we incorporate the principles of iterative expansion used in the literature [TALG 2012] to obtain a better algorithm for 3D-matching, with a running time of O ∗ (2.003 (3k)). Apart from the significantly improved running times, we believe that these algorithms demonstrate an interesting application of representative families in conjunction with more traditional techniques

    Induced Sputum Nitrite Levels Correlate with Clinical Asthma Parameters in Children Aged 7–18 Years with Mild to Moderate Persistent Asthma

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    Purpose: The objective of this study is to measure levels of nitrites in induced sputum in children with asthma and correlate it with clinical asthma parameters. Method: This prospective observational study was done in PGIMER, Dr. Ram Manohar Lohia Hospital, New Delhi, on 91 children aged 7-18 years with mild and moderate persistent asthma. Patients were specifically evaluated for five clinical parameters of asthma (i.e. Days of acute exacerbations, use of salbutamol as rescue medication, emergency visits, nights with cough, days of school absence) and induced sputum nitrite levels was done at the time of enrollment and 3 months after treatment with inhaled budesonide. Results: The mean age of subjects was 10.79 ± 2.563yrs. Six (6.59%) patients were not able to perform induced sputum, eighty five (93.41%) patients were suitable for data analysis. There was significant reduction in sputum nitrite levels from 33.42 ± 22.04nmol/ml at enrollment to 11.72 ± 5.61 nmol/ml (P < 0.0005) after 3 months of inhaled budesonide therapy. Significant positive correlation was found between reduction in sputum nitrite level and control of asthma symptoms: Days of acute exacerbations(r value = 0.548, P value = 0.0001), Days of salbutamol use as rescue medication (r value = 0.431, P value =< 0.0001), Number of emergency visits(r value = 0.414, P value = 0.0001), Nights with cough (r value = 0.259, P value = 0.0169), Days of school absence(r value = 0.411, P value = 0.0001). Sputum nitrite levels were significantly higher in moderate persistent asthmatics as compared to mild at the time of enrollment (P < 0.0005), which shows that induced sputum nitrite levels correlate with asthma severity. Conclusions: This study confirms that nitrites in induced sputum correlate well with clinical asthma parameters and asthma severity in children and is a simple, non invasive, and cheap method which can be used as a parameter for monitoring of asthma

    DETERMINISTIC ALGORITHMS FOR MATCHING AND PACKING PROBLEMS BASED ON REPRESENTATIVE SETS

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    In this work, we study the well-known r-DIMENSIONAL k-MATCHING ((r, k)-DM), and r-SET k-PACKING ((r, k)-SP) problems. Given a universe U := U-1 ... U-r and an r-uniform family F subset of U-1 x ... x U-r, the (r, k)-DM problem asks if F admits a collection of k mutually disjoint sets. Given a universe U and an r-uniform family F subset of 2(U), the (r, k)-SP problem asks if F admits a collection of k mutually disjoint sets. We employ techniques based on dynamic programming and representative families. This leads to a deterministic algorithm with running time O(2.851((r-1)k) .vertical bar F vertical bar. n log(2)n . logW) for the weighted version of (r, k)-DM, where W is the maximum weight in the input, and a deterministic algorithm with running time O(2.851((r-0.5501)k).vertical bar F vertical bar.n log(2) n . logW) for the weighted version of (r, k)-SP. Thus, we significantly improve the previous best known deterministic running times for (r, k)-DM and (r, k)-SP and the previous best known running times for their weighted versions. We rely on structural properties of (r, k)-DM and (r, k)-SP to develop algorithms that are faster than those that can be obtained by a standard use of representative sets. Incorporating the principles of iterative expansion, we obtain a better algorithm for (3, k)-DM, running in time O(2.004(3k).vertical bar F vertical bar . n log(2)n). We believe that this algorithm demonstrates an interesting application of representative families in conjunction with more traditional techniques. Furthermore, we present kernels of size O(e(r)r(k-1)(r) logW) for the weighted versions of (r, k)-DM and (r, k)-SP, improving the previous best known kernels of size O(r!r(k-1)(r) logW) for these problems

    Finding even subgraphs even faster

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    In the UNDIRECTED EULERIAN EDGE DELETION problem, we are given an undirected graph and an integer k, and the objective is to delete k edges such that the resultant graph is a connected graph in which all the vertices have even degrees. The corresponding problem in digraphs where the resulting graph should be strongly connected and every vertex should have the same in-degree as its out-degree is called DIRECTED EULERIAN EDGE DELETION. In this paper, using the technique of computing representative families of co-graphic matroids we design algorithms which solve these problems in time 2(O(k))n(O(1)), improving the algorithms by Cygan et al. Algorithmica, 2014] and affirmatively answer the open problem posed by them. The crucial insight we bring to these problems is to view the solution as an independent set of a co-graphic matroid. (C) 2018 Elsevier Inc. All rights reserved
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