Minimizing the Size of the Uncertainty Regions for Centers of Moving Entities

In this paper, we study the problems of computing the 1-center, centroid, and 1-median of objects moving with bounded speed in Euclidean space. We can acquire the exact location of only a constant number of objects (usually one) per unit time, but for every other object, its set of potential locations, called the object's uncertainty region, grows subject only to the speed limit. As a result, the center of the objects may be at several possible locations, called the center's uncertainty region. For each of these center problems, we design query strategies to minimize the size of the center's uncertainty region and compare its performance to an optimal query strategy that knows the trajectories of the objects, but must still query to reduce their uncertainty. For the static case of the 1-center problem in R^1, we show an algorithm that queries four objects per unit time and is 1-competitive against the optimal algorithm with one query per unit time. For the general case of the 1-center problem in R^1, the centroid problem in R^d, and the 1-median problem in R^1, we prove that the Round-robin scheduling algorithm is the best possible competitive algorithm. For the center of mass problem in R^d, we provide an O(log n)-competitive algorithm. In addition, for the general case of the 1-center problem in R^d (d >= 2), we argue that no algorithm can guarantee a bounded competitive ratio against the optimal algorithm.Comment: 22 pages, 3 figures, accepted to LATIN 202

On the Feasibility of Social Network-based Pollution Sensing in ITSs

Intense vehicular traffic is recognized as a global societal problem, with a multifaceted influence on the quality of life of a person. Intelligent Transportation Systems (ITS) can play an important role in combating such problem, decreasing pollution levels and, consequently, their negative effects. One of the goals of ITSs, in fact, is that of controlling traffic flows, measuring traffic states, providing vehicles with routes that globally pursue low pollution conditions. How such systems measure and enforce given traffic states has been at the center of multiple research efforts in the past few years. Although many different solutions have been proposed, very limited effort has been devoted to exploring the potential of social network analysis in such context. Social networks, in general, provide direct feedback from people and, as such, potentially very valuable information. A post that tells, for example, how a person feels about pollution at a given time in a given location, could be put to good use by an environment aware ITS aiming at minimizing contaminant emissions in residential areas. This work verifies the feasibility of using pollution related social network feeds into ITS operations. In particular, it concentrates on understanding how reliable such information is, producing an analysis that confronts over 1,500,000 posts and pollution data obtained from on-the- field sensors over a one-year span.Comment: 10 pages, 15 figures, Transaction Forma

Constrained Clustering Problems and Parity Games

Clustering is a fundamental tool in data mining. It partitions points into groups (clusters) and may be used to make decisions for each point based on its group. We study several clustering objectives. We begin with studying the Euclidean k-center problem. The k-center problem is a classical combinatorial optimization problem which asks to select k centers and assign each input point in a set P to one of the centers, such that the maximum distance of any input point to its assigned center is minimized. The Euclidean k-center problem assumes that the input set P is a subset of a Euclidean space and that each location in the Euclidean space can be chosen as a center. We focus on the special case with k = 1, the smallest enclosing ball problem: given a set of points in m-dimensional Euclidean space, find the smallest sphere enclosing all the points. We combine known results about convex optimization with structural properties of the smallest enclosing ball to create a new algorithm. We show that on instances with rational coefficients our new algorithm computes the exact center of the optimal solutions and has a worst-case run time that is polynomial in the size of the input. We use the new algorithm to show that we can solve the Euclidean k-center problem in polynomial time for constant k and dimension m. The general unconstrained clustering problems are mostly very well studied. The k-center problem for example allows for elegant 2-approximation algorithms(Gonzalez 1985, Hochbaum,Shmoys 1986). However, the situation becomes significantly more difficult when constraints are added to the problem. We first look at the fair clustering. The fairness constraint is motivated by the fact that the general process of computing a clustering may harm protected (minority) classes if the clustering algorithm does not adequately represent them in desirable clusters -- especially if the data is already biased. At NIPS 2017, Chierichetti et al. proposed a model for fair clustering requiring the representation in each cluster to (approximately) preserve the global fraction of each protected class. Restricting to two protected classes, they developed both a 4-approximation algorithm for the fair k-center problem and an O(t)-approximation algorithm for the fair k-median problem, where t is a parameter for the fairness model. For multiple protected classes, the best known result is a 14-approximation algorithm for fair k-center (Rösner, Schmidt 2018). We extend and improve the known results. Firstly, we give a 5-approximation algorithm for the fair k-center problem with multiple protected classes. Secondly, we propose a relaxed fairness notion under which we can give bicriteria constant-factor approximation algorithms for the fair version of all of the classical clustering objectives (k-center, k-supplier, k-median, k-means and facility location). The latter approximation algorithms are achieved by a framework that takes an arbitrary existing unfair (integral) solution and a fair (fractional) LP solution and combines them into an essentially fair clustering with a weakly supervised rounding scheme. In this way, a fair clustering can be established belatedly, in a situation where for example the centers are already fixed. The second clustering constraint we study is privacy: Here, we are asked to only open a center when at least l points will be assigned to it. We raise the question whether a general method can be derived to turn an approximation algorithm for a clustering problem with some constraints into an approximation algorithm that additionally respects privacy. We show how to combine privacy with several other constraints and obtain approximation algorithms for the k-center problem with several combinations of constraints. In this dissertation we also study parity games, a two player game played on a directed graph. We study the case in which one of the two players controls only a small number k of nodes and the other player controls the n-k other nodes of the game. Our main result is a fixed-parameter-tractable algorithm that solves bipartite parity games in time k^{O(sqrt{k})} O(n^3), and general parity games in time (p+k)^{O(sqrt{k})} O(pnm), where p is the number of distinct priorities and m is the number of edges. For all games with k = o(n) this improves the previously fastest algorithm by Jurdziński, Paterson, and Zwick (2008). We also obtain novel kernelization results and an improved deterministic algorithm for parity games on graphs with small average node-degree

FPT Approximation for Fair Minimum-Load Clustering

In this paper, we consider the Minimum-Load k-Clustering/Facility Location (MLkC) problem where we are given a set P of n points in a metric space that we have to cluster and an integer k > 0 that denotes the number of clusters. Additionally, we are given a set F of cluster centers in the same metric space. The goal is to select a set C ? F of k centers and assign each point in P to a center in C, such that the maximum load over all centers is minimized. Here the load of a center is the sum of the distances between it and the points assigned to it. Although clustering/facility location problems have rich literature, the minimum-load objective has not been studied substantially, and hence MLkC has remained a poorly understood problem. More interestingly, the problem is notoriously hard even in some special cases including the one in line metrics as shown by Ahmadian et al. [APPROX 2014, ACM Trans. Algorithms 2018]. They also show APX-hardness of the problem in the plane. On the other hand, the best-known approximation factor for MLkC is O(k), even in the plane. In this work, we study a fair version of MLkC inspired by the work of Chierichetti et al. [NeurIPS, 2017]. Here the input points are partitioned into ? protected groups, and only clusters that proportionally represent each group are allowed. MLkC is the special case with ? = 1. For the fair version, we are able to obtain a randomized 3-approximation algorithm in f(k,?)? n^O(1) time. Also, our scheme leads to an improved (1 + ?)-approximation in the case of Euclidean norm with the same running time (depending also linearly on the dimension d). Our results imply the same approximations for MLkC with running time f(k)? n^O(1), achieving the first constant-factor FPT approximations for this problem in general and Euclidean metric spaces

FPT Approximation for Fair Minimum-Load Clustering

In this paper, we consider the Minimum-Load k-Clustering/Facility Location (MLkC) problem where we are given a set P of n points in a metric space that we have to cluster and an integer k > 0 that denotes the number of clusters. Additionally, we are given a set F of cluster centers in the same metric space. The goal is to select a set C ? F of k centers and assign each point in P to a center in C, such that the maximum load over all centers is minimized. Here the load of a center is the sum of the distances between it and the points assigned to it. Although clustering/facility location problems have rich literature, the minimum-load objective has not been studied substantially, and hence MLkC has remained a poorly understood problem. More interestingly, the problem is notoriously hard even in some special cases including the one in line metrics as shown by Ahmadian et al. [APPROX 2014, ACM Trans. Algorithms 2018]. They also show APX-hardness of the problem in the plane. On the other hand, the best-known approximation factor for MLkC is O(k), even in the plane. In this work, we study a fair version of MLkC inspired by the work of Chierichetti et al. [NeurIPS, 2017]. Here the input points are partitioned into ? protected groups, and only clusters that proportionally represent each group are allowed. MLkC is the special case with ? = 1. For the fair version, we are able to obtain a randomized 3-approximation algorithm in f(k,?)? n^O(1) time. Also, our scheme leads to an improved (1 + ?)-approximation in the case of Euclidean norm with the same running time (depending also linearly on the dimension d). Our results imply the same approximations for MLkC with running time f(k)? n^O(1), achieving the first constant-factor FPT approximations for this problem in general and Euclidean metric spaces

Management of Cutaneous Malignancy - A Review

Skin cancer is the most frequent type of cancer, accounting for about 20% of all cancers in the State of Virginia, and the most common type of skin cancer is the basal cell carcinoma. The basal cell carcinoma is a tumor which is not considered highly malignant because, in general, it does not metastasize, although there have been a few instances in which metastases have occurred. However, such lesions may be quite destructive at times. The typical basal cell carcinoma presents as a waxy, papular or nodular lesion which has a gelatinous or somewhat translucent appearance. Coursing across the surface from the normal skin toward the center of the lesion, one will often see fine telangiectatic vessels. At times the lesions may be somewhat deceptive because of their location, and this is particularly true in the inner canthus where they may be missed until they are fairly large. Some basal cell carcinomas will remain relatively quiescent for long periods of time; others will become much more aggressive and grow rapidly. The tumor may, at times, be much like an iceberg with only the tip appearing, and this is particularly a problem with lesions on the nose. In treating a lesion in this location one has to be very cautious and be prepared to perform grafting, if this is required. It may, at times, be difficult to differentiate a basal cell carcinoma from small lesions which we call sebaceous adenomas, which occur frequently on the faces of elderly individuals. These are small waxy, creamy elevations usually on the forehead and they are the result of hyperplasia of sebaceous follicles

Gergunung Sport Center Klaten

The needs of the Klaten district for Sport Centers are motivated by the lack of standardized sports facilities in Klaten that can accommodate all sports activities in Klaten. The problem that needs attention is that the sports facilities in Klaten Regency are mostly scattered, making it very difficult for the government or sponsors to provide guidance for certain athletes or clubs. Facing this phenomenon, athletes, clubs and sports fans need repetitive forums where they can carry out activities such as training to improve achievement, improve physical fitness as well as recreation. Therefore in the lack of it arises a thought to provide a facility that is able to accommodate these activities in one integrated location in the form of a Sports Center. Location Sport Center is located in Gergunung, Klaten Utara District. Gergunung is one of the villages in the northern Klaten sub-district, which in the Klaten Regency Regional Spatial Plan, Klaten Utara sub-district is included in the sub-district which is the Regional Activity Center. The development of Sports today is greatly influenced by the progress of the world by sport in accordance with the development of the era in which the sport was born and also in accordance with the needs of the general public activities. To get a design in the form of sports facilities that accommodate and have national standards. Therefore it is necessary to have a literature study on sports buildings that facilitate the design with sketches of images and documentation. Gergunung Sport center is designed with modern architectural style and with the concept of nature

GEO-REPLICATION IN A REVIEW OF LATENCY AND COST-EFFECTIVENESS

Replication is a data distribution technique for synchronization between databases so that data remains consistent. Replication can overcome data loss problems and perform system recovery quickly if a problem occurs on one of the servers. One of the problems is when a natural disaster occurs at the server location. As a result, if you do not have data replication in different locations, it will cause the system to not run and possibly lose data. Then, geo-replication can reduce latency because the distance between the client and the data center is much closer. The application of geo-replication in general replicates data in all data centers. As a result, the cost of implementation is high because it requires a lot of resources. Because of the various advantages and disadvantages in its application, it is necessary to group geo-replication techniques to make it easier for researchers and technicians to adjust as needed. Therefore, this paper surveys the articles on Geo-replication techniques to implement cost-effectiveness and latency. The articles surveyed included a method for selecting replication sites, a method for reducing round trip time, a method according to data type, and selecting a leader to determine which server node to use. The results of the article survey show that implementing geo-replication for cost-effectiveness is more suitable for use in systems where all users do not need to access all data. Meanwhile, low latency is more suitable for systems used by various types of users. This paper can utilize the techniques that have been reviewed to overcome the problem of cost-effectiveness and latency in implementing Geo-replication

Hub Location Problem with Allowed Routing between Nonhub Nodes

In this study, we relax one of the general assumptions in the hub location literature by allowing routed flows between nonhub nodes. In hub networks, different flows are consolidated and routed via collection, interhub, and distribution arcs. Due to consolidation, some flows travel long paths despite closeness of their origin and destination. In this study, we allow direct flows by penalizing by a scalar factor of original cost of transshipment between these arcs. We present mathematical models for median, center, and set covering versions of the problem for single- and multi-allocation cases. We test the models with the CAB and TR data sets. We discuss the properties of established direct connections for different models by using another mathematical model where the number of direct flows is bounded and interpret the effect of changes in problem parameters. © 2015 by The Ohio State University