Sapna Grover - Academia.edu (original) (raw)

Papers by Sapna Grover

arXiv (Cornell University), Mar 26, 2022

Clustering is one of the most fundamental problem in Machine Learning. Researchers in the field o... more Clustering is one of the most fundamental problem in Machine Learning. Researchers in the field often require a lower bound on the size of the clusters to maintain anonymity and upper bound for the ease of analysis. Specifying an optimal cluster size is a problem often faced by scientists. In this paper, we present a framework to obtain constant factor approximations for some prominent clustering objectives, with lower and upper bounds on cluster size. This enables scientists to give an approximate cluster size by specifying the lower and the upper bounds for it. Our results preserve the lower bounds but may violate the upper bound a little. We also reduce the violation in upper bounds for a special case when the gap between the lower and upper bounds is not too small.

16 In this paper, we give the first constant factor approximation algorithm for capacitated knaps... more 16 In this paper, we give the first constant factor approximation algorithm for capacitated knapsack 17 median problem (CKnM) for hard uniform capacities, violating the budget by a factor of 1 + 18 and capacities by a 2 + factor. To the best of our knowledge, no constant factor approximation 19 is known for the problem even with capacity/budget/both violations. Even for the uncapacitated 20 variant of the problem, the natural LP is known to have an unbounded integrality gap even after 21 adding the covering inequalities to strengthen the LP. Our techniques for CKnM provide two 22 types of results for the capacitated k-facility location problem. We present an O(1/ 2) factor 23 approximation for the problem, violating capacities by (2+ ). Another result is an O(1/ ) factor 24 approximation, violating the capacities by a factor of at most (1+ ) using at most 2k facilities for 25 a fixed > 0. As a by-product, a constant factor approximation algorithm for capacitated facility 26 locat...

Delay Tolerant Networks are the network where the continuous network connectivity is lacking. R-C... more Delay Tolerant Networks are the network where the continuous network connectivity is lacking. R-CAR algorithm(2) addresses the issue of routing in such networks. But the paper fails to address issues regarding newly arrived node in a network, prioritization of low hop count carrier node and sharing and dynamic updation of local reputation tables. This paper gives an Improved version (IRCAR) that efficiently solves these issues.

Delay-tolerant networking (DTN) is an approach to computer network architecture that seeks to add... more Delay-tolerant networking (DTN) is an approach to computer network architecture that seeks to address the technical issues in heterogeneous networks which may lack continuous network connectivity. Traditional routing algorithms try to establish a complete route from source to destination and then forward actual data. Due to lack of end to end connectivity, this is not possible in DTN. Also, security guarantees are difficult to establish in a network without persistent connectivity. This paper gives a fast greedy algorithm that intelligently selects next carrier node(s), optimizing the chances of successful delivery.

ArXiv, 2021

With growing emphasis on e-commerce marketplace platforms where we have a central platform mediat... more With growing emphasis on e-commerce marketplace platforms where we have a central platform mediating between the seller and the buyer, it becomes important to keep a check on the availability and profitability of the central store. A store serving too less clients can be non-profitable and a store getting too many orders can lead to bad service to the customers which can be detrimental for the business. In this paper, we study the facility location problem(FL) with upper and lower bounds on the number of clients an open facility serves. Constant factor approximations are known for the restricted variants of the problem with only the upper bounds or only the lower bounds. The only work that deals with bounds on both the sides violates both the bounds [8]. In this paper, we present the first (constant factor) approximation for the problem violating the upper bound by a factor of (5/2) without violating the lower bounds when both the lower and the upper bounds are uniform. We first giv...

Routing in Delay Tolerant Network has received considerable attention in the recent years. Contex... more Routing in Delay Tolerant Network has received considerable attention in the recent years. Context-aware Adaptive routing and Reputation based Context-aware Adaptive routing are based on a single copy of the message, whose delivery is based on the choice of a best carrier node. In this paper, we present a comparative analysis of these algorithms and highlight the issues not addressed by any of these algorithm.

Lecture Notes in Computer Science, 2021

International Journal of Innovative Research and Development, Jun 3, 2014

The notion of 'software engineering' was first proposed in 1968, defining best practices ... more The notion of 'software engineering' was first proposed in 1968, defining best practices for software development, grounded in the application of engineering. Though, the key areas of software engineering process are identified as specification, development, validation and evolution by every process model, little attention is paid to specification and designing as compared to development, testing and maintenance. In this paper, we consider few case studies where negligence during requirements engineering and faulty design led to heavy causalities.

International Journal of Innovative Research and Development, May 30, 2014

The traditional notion of software lies in plan-driven model of development. However, agile devel... more The traditional notion of software lies in plan-driven model of development. However, agile development methods universally rely on updating and improving the plan along with the passage of time. They are best suited for application development where the system requirements usually change rapidly during development. Suited for small sized teams and small projects, agile development cannot be easily applied in large companies with large projects. Much work has been done in past to scale the agile development techniques. In this paper, we discuss scaled agile development framework, highlighting the problems associated with this scaling.

Informatica, 2018

In this paper, we study the hard uniform capacitated k-median problem using local search heuristi... more In this paper, we study the hard uniform capacitated k-median problem using local search heuristic. Obtaining a constant factor approximation for the problem is open. All the existing solutions giving constantfactor approximation, violate at least one of the constraints (cardinality/ capacity). All except Koruplou et al. [22] are based on LP-relaxation. We give (3 +) factor approximation algorithm for the problem violating the cardinality by a factor of 8/3 ≈ 2.67. There is a trade-off between the approximation factor and the cardinality violation between our work and the existing work. Koruplou et al. [22] gave (1 + α) approximation factor with (5+5/α) factor loss in cardinality using local search paradigm. Though the approximation factor can be made arbitrarily small, cardinality loss is at least 5. On the other hand, we improve upon the result of Aardal et al. [1] in terms of factor-loss. They gave (7+) factor approximation, with the cardinality violation by a factor 2. Most importantly, their result is obtained using LP-rounding, whereas local search techniques are straightforward, simple to apply and have been shown to perform well in practice via empirical studies. We extend the result to hard uniform capacitated k-median with penalties. To the best of our knowledge, ours is the first result for the problem.

arXiv (Cornell University), Mar 26, 2022

Clustering is one of the most fundamental problem in Machine Learning. Researchers in the field o... more Clustering is one of the most fundamental problem in Machine Learning. Researchers in the field often require a lower bound on the size of the clusters to maintain anonymity and upper bound for the ease of analysis. Specifying an optimal cluster size is a problem often faced by scientists. In this paper, we present a framework to obtain constant factor approximations for some prominent clustering objectives, with lower and upper bounds on cluster size. This enables scientists to give an approximate cluster size by specifying the lower and the upper bounds for it. Our results preserve the lower bounds but may violate the upper bound a little. We also reduce the violation in upper bounds for a special case when the gap between the lower and upper bounds is not too small.

16 In this paper, we give the first constant factor approximation algorithm for capacitated knaps... more 16 In this paper, we give the first constant factor approximation algorithm for capacitated knapsack 17 median problem (CKnM) for hard uniform capacities, violating the budget by a factor of 1 + 18 and capacities by a 2 + factor. To the best of our knowledge, no constant factor approximation 19 is known for the problem even with capacity/budget/both violations. Even for the uncapacitated 20 variant of the problem, the natural LP is known to have an unbounded integrality gap even after 21 adding the covering inequalities to strengthen the LP. Our techniques for CKnM provide two 22 types of results for the capacitated k-facility location problem. We present an O(1/ 2) factor 23 approximation for the problem, violating capacities by (2+ ). Another result is an O(1/ ) factor 24 approximation, violating the capacities by a factor of at most (1+ ) using at most 2k facilities for 25 a fixed > 0. As a by-product, a constant factor approximation algorithm for capacitated facility 26 locat...

Delay Tolerant Networks are the network where the continuous network connectivity is lacking. R-C... more Delay Tolerant Networks are the network where the continuous network connectivity is lacking. R-CAR algorithm(2) addresses the issue of routing in such networks. But the paper fails to address issues regarding newly arrived node in a network, prioritization of low hop count carrier node and sharing and dynamic updation of local reputation tables. This paper gives an Improved version (IRCAR) that efficiently solves these issues.

Delay-tolerant networking (DTN) is an approach to computer network architecture that seeks to add... more Delay-tolerant networking (DTN) is an approach to computer network architecture that seeks to address the technical issues in heterogeneous networks which may lack continuous network connectivity. Traditional routing algorithms try to establish a complete route from source to destination and then forward actual data. Due to lack of end to end connectivity, this is not possible in DTN. Also, security guarantees are difficult to establish in a network without persistent connectivity. This paper gives a fast greedy algorithm that intelligently selects next carrier node(s), optimizing the chances of successful delivery.

ArXiv, 2021

With growing emphasis on e-commerce marketplace platforms where we have a central platform mediat... more With growing emphasis on e-commerce marketplace platforms where we have a central platform mediating between the seller and the buyer, it becomes important to keep a check on the availability and profitability of the central store. A store serving too less clients can be non-profitable and a store getting too many orders can lead to bad service to the customers which can be detrimental for the business. In this paper, we study the facility location problem(FL) with upper and lower bounds on the number of clients an open facility serves. Constant factor approximations are known for the restricted variants of the problem with only the upper bounds or only the lower bounds. The only work that deals with bounds on both the sides violates both the bounds [8]. In this paper, we present the first (constant factor) approximation for the problem violating the upper bound by a factor of (5/2) without violating the lower bounds when both the lower and the upper bounds are uniform. We first giv...

Routing in Delay Tolerant Network has received considerable attention in the recent years. Contex... more Routing in Delay Tolerant Network has received considerable attention in the recent years. Context-aware Adaptive routing and Reputation based Context-aware Adaptive routing are based on a single copy of the message, whose delivery is based on the choice of a best carrier node. In this paper, we present a comparative analysis of these algorithms and highlight the issues not addressed by any of these algorithm.

Lecture Notes in Computer Science, 2021

International Journal of Innovative Research and Development, Jun 3, 2014

The notion of 'software engineering' was first proposed in 1968, defining best practices ... more The notion of 'software engineering' was first proposed in 1968, defining best practices for software development, grounded in the application of engineering. Though, the key areas of software engineering process are identified as specification, development, validation and evolution by every process model, little attention is paid to specification and designing as compared to development, testing and maintenance. In this paper, we consider few case studies where negligence during requirements engineering and faulty design led to heavy causalities.

International Journal of Innovative Research and Development, May 30, 2014

The traditional notion of software lies in plan-driven model of development. However, agile devel... more The traditional notion of software lies in plan-driven model of development. However, agile development methods universally rely on updating and improving the plan along with the passage of time. They are best suited for application development where the system requirements usually change rapidly during development. Suited for small sized teams and small projects, agile development cannot be easily applied in large companies with large projects. Much work has been done in past to scale the agile development techniques. In this paper, we discuss scaled agile development framework, highlighting the problems associated with this scaling.

Informatica, 2018

In this paper, we study the hard uniform capacitated k-median problem using local search heuristi... more In this paper, we study the hard uniform capacitated k-median problem using local search heuristic. Obtaining a constant factor approximation for the problem is open. All the existing solutions giving constantfactor approximation, violate at least one of the constraints (cardinality/ capacity). All except Koruplou et al. [22] are based on LP-relaxation. We give (3 +) factor approximation algorithm for the problem violating the cardinality by a factor of 8/3 ≈ 2.67. There is a trade-off between the approximation factor and the cardinality violation between our work and the existing work. Koruplou et al. [22] gave (1 + α) approximation factor with (5+5/α) factor loss in cardinality using local search paradigm. Though the approximation factor can be made arbitrarily small, cardinality loss is at least 5. On the other hand, we improve upon the result of Aardal et al. [1] in terms of factor-loss. They gave (7+) factor approximation, with the cardinality violation by a factor 2. Most importantly, their result is obtained using LP-rounding, whereas local search techniques are straightforward, simple to apply and have been shown to perform well in practice via empirical studies. We extend the result to hard uniform capacitated k-median with penalties. To the best of our knowledge, ours is the first result for the problem.