piyush kumar | Uttar Pradesh Technical University (original) (raw)

Papers by piyush kumar

Research paper thumbnail of Computing Core-Sets and Approximate Smallest Enclosing HyperSpheres in High Dimensions

We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions.... more We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Using techniques of second-order cone programming and "coresets", we have developed (1 + )-approximation algorithms that perform well in practice, especially for very high dimensions, in addition to having provable guarantees. We prove the existence of core-sets of size O(1/ ), improving the previous bound of O(1/ 2 ), and we study empirically how the core-set size grows with dimension. We show that our algorithm, which is simple to implement, results in fast computation of nearly optimal solutions for point sets in much higher dimension than previously computable using exact techniques.

Research paper thumbnail of Minimum-Volume Enclosing Ellipsoids and Core Sets

Journal of Optimization Theory and Applications, 2005

We study the problem of computing a (1+ε)-approximation to the minimum-volume enclosing ellipsoid... more We study the problem of computing a (1+ε)-approximation to the minimum-volume enclosing ellipsoid of a given point set calS=p1,p2,dots,pnsubseteqmathbbRd{\cal S} = \{p^{1}, p^{2}, \dots, p^{n}\} \subseteq {\mathbb R}^{d}calS=p1,p2,dots,pnsubseteqmathbbRd . Based on a simple, initial volume approximation method, we propose a modification of the Khachiyan first-order algorithm. Our analysis leads to a slightly improved complexity bound of O(nd3/epsilon)O(nd^{3}/\epsilon)O(nd3/epsilon) operations for epsilonin(0,1)\epsilon \in(0, 1)epsilonin(0,1) . As a byproduct, our algorithm returns a core set calXsubseteqcalS{\cal X} \subseteq {\cal S}calXsubseteqcalS with the property that the minimum-volume enclosing ellipsoid of calX{\cal X}calX provides a good approximation to that of calS{\cal S}calS . Furthermore, the size of calX{\cal X}calX depends on only the dimension d and ε, but not on the number of points n. In particular, our results imply that vertcalXvert=O(d2/epsilon)\vert {\cal X} \vert = O(d^{2}/\epsilon)vertcalXvert=O(d2/epsilon) for epsilonin(0,1)\epsilon \in(0, 1)epsilonin(0,1) .

Research paper thumbnail of Comuting Core-Sets and Approximate Smallest Enclosing HyperSpheres in High Dimensions

Abstract: We study the minimum enclosing ball (MEB) problemfor sets of points or balls in high di... more Abstract: We study the minimum enclosing ball (MEB) problemfor sets of points or balls in high dimensions. Usingtechniques of second-order cone programming and "coresets", we have developed (1 + #)-approximation algorithmsthat perform well in practice, especially for very highdimensions, in addition to having provable guarantees. Weprove the existence of core-sets of size O(1/#), improvingthe previous bound of O(1/#), and we

Research paper thumbnail of Approximate minimum enclosing balls in high dimensions using core-sets

ACM Journal of Experimental Algorithms, 2003

We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions.... more We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Using techniques of second-order cone programming and "core-sets", we have developed (1 + )-approximation algorithms that perform well in practice, especially for very high dimensions, in addition to having provable guarantees. We prove the existence of core-sets of size O(1/ ), improving the previous bound of O(1/ 2 ), and we study empirically how the core-set size grows with dimension. We show that our algorithm, which is simple to implement, results in fast computation of nearly optimal solutions for point sets in much higher dimension than previously computable using exact techniques.

Research paper thumbnail of Minimum-Volume Enclosing Ellipsoids and Core

Abstract. We study the problem of computing a (1 + )-approximation to the minimum volume enclosin... more Abstract. We study the problem of computing a (1 + )-approximation to the minimum volume enclosing ellipsoid of a given point set S = {p,/ ) for 2 (0,1). Key Words: L¨owner ellipsoids, core sets, approximation algorithms. 2

Research paper thumbnail of Accurate localization of RFID tags using phase difference

... Cory Hekimian-Williams, Brandon Grant, Xiuwen Liu, Zhenghao Zhang, and Piyush Kumar Departmen... more ... Cory Hekimian-Williams, Brandon Grant, Xiuwen Liu, Zhenghao Zhang, and Piyush Kumar Department of Computer Science, Florida State University ... plot study system that consists of active RFID tags, Universal Software Radio Peripheral (USRP) as receivers, and a pan-tilt unit ...

Research paper thumbnail of Computing Core-Sets and Approximate Smallest Enclosing HyperSpheres in High Dimensions

We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions.... more We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Using techniques of second-order cone programming and "coresets", we have developed (1 + )-approximation algorithms that perform well in practice, especially for very high dimensions, in addition to having provable guarantees. We prove the existence of core-sets of size O(1/ ), improving the previous bound of O(1/ 2 ), and we study empirically how the core-set size grows with dimension. We show that our algorithm, which is simple to implement, results in fast computation of nearly optimal solutions for point sets in much higher dimension than previously computable using exact techniques.

Research paper thumbnail of Minimum-Volume Enclosing Ellipsoids and Core Sets

Journal of Optimization Theory and Applications, 2005

We study the problem of computing a (1+ε)-approximation to the minimum-volume enclosing ellipsoid... more We study the problem of computing a (1+ε)-approximation to the minimum-volume enclosing ellipsoid of a given point set calS=p1,p2,dots,pnsubseteqmathbbRd{\cal S} = \{p^{1}, p^{2}, \dots, p^{n}\} \subseteq {\mathbb R}^{d}calS=p1,p2,dots,pnsubseteqmathbbRd . Based on a simple, initial volume approximation method, we propose a modification of the Khachiyan first-order algorithm. Our analysis leads to a slightly improved complexity bound of O(nd3/epsilon)O(nd^{3}/\epsilon)O(nd3/epsilon) operations for epsilonin(0,1)\epsilon \in(0, 1)epsilonin(0,1) . As a byproduct, our algorithm returns a core set calXsubseteqcalS{\cal X} \subseteq {\cal S}calXsubseteqcalS with the property that the minimum-volume enclosing ellipsoid of calX{\cal X}calX provides a good approximation to that of calS{\cal S}calS . Furthermore, the size of calX{\cal X}calX depends on only the dimension d and ε, but not on the number of points n. In particular, our results imply that vertcalXvert=O(d2/epsilon)\vert {\cal X} \vert = O(d^{2}/\epsilon)vertcalXvert=O(d2/epsilon) for epsilonin(0,1)\epsilon \in(0, 1)epsilonin(0,1) .

Research paper thumbnail of Comuting Core-Sets and Approximate Smallest Enclosing HyperSpheres in High Dimensions

Abstract: We study the minimum enclosing ball (MEB) problemfor sets of points or balls in high di... more Abstract: We study the minimum enclosing ball (MEB) problemfor sets of points or balls in high dimensions. Usingtechniques of second-order cone programming and "coresets", we have developed (1 + #)-approximation algorithmsthat perform well in practice, especially for very highdimensions, in addition to having provable guarantees. Weprove the existence of core-sets of size O(1/#), improvingthe previous bound of O(1/#), and we

Research paper thumbnail of Approximate minimum enclosing balls in high dimensions using core-sets

ACM Journal of Experimental Algorithms, 2003

We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions.... more We study the minimum enclosing ball (MEB) problem for sets of points or balls in high dimensions. Using techniques of second-order cone programming and "core-sets", we have developed (1 + )-approximation algorithms that perform well in practice, especially for very high dimensions, in addition to having provable guarantees. We prove the existence of core-sets of size O(1/ ), improving the previous bound of O(1/ 2 ), and we study empirically how the core-set size grows with dimension. We show that our algorithm, which is simple to implement, results in fast computation of nearly optimal solutions for point sets in much higher dimension than previously computable using exact techniques.

Research paper thumbnail of Minimum-Volume Enclosing Ellipsoids and Core

Abstract. We study the problem of computing a (1 + )-approximation to the minimum volume enclosin... more Abstract. We study the problem of computing a (1 + )-approximation to the minimum volume enclosing ellipsoid of a given point set S = {p,/ ) for 2 (0,1). Key Words: L¨owner ellipsoids, core sets, approximation algorithms. 2

Research paper thumbnail of Accurate localization of RFID tags using phase difference

... Cory Hekimian-Williams, Brandon Grant, Xiuwen Liu, Zhenghao Zhang, and Piyush Kumar Departmen... more ... Cory Hekimian-Williams, Brandon Grant, Xiuwen Liu, Zhenghao Zhang, and Piyush Kumar Department of Computer Science, Florida State University ... plot study system that consists of active RFID tags, Universal Software Radio Peripheral (USRP) as receivers, and a pan-tilt unit ...