Amit Kumar - Academia.edu (original) (raw)

Papers by Amit Kumar

We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {... more We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {c e } on the edges, a set of facilities F ⊆ V , and a set of clients D ⊆ V . Facility i has a facility opening cost f i and client j has d j units of demand. We are also given a parameter M ≥ 1. A solution opens some facilities, say F , assigns each client j to an open facility i(j), and connects the open facilities by a Steiner tree T . The total cost incurred is i∈F f i + j∈D d j c i(j)j + M e∈T c e . We want a solution of minimum cost.

We give simple and easy-to-analyze randomized approximation algorithms for several well-studied N... more We give simple and easy-to-analyze randomized approximation algorithms for several well-studied NP-hard network design problems. Our algorithms improve over the previously best known approximation ratios. Our main results are the following.

Computer Communication Review, 2001

Virtual Private Networks (VPNs) provide customers with predictable and secure network connections... more Virtual Private Networks (VPNs) provide customers with predictable and secure network connections over a shared network. The recently proposed hose model for VPNs allows for greater flexibility since it permits traffic to and from a hose endpoint to be arbitrarily distributed to other endpoints. In this paper, we develop novel algorithms for provisioning VPNs in the hose model. We connect VPN endpoints using a tree structure and our algorithms attempt to optimize the total bandwidth reserved on edges of the VPN tree. We show that even for the simple scenario in which network links are assumed to have infinite capacity, the general problem of computing the optimal VPN tree is NP-hard. Fortunately, for the special case when the ingress and egress bandwidths for each VPN endpoint are equal, we can devise an algorithm for computing the optimal tree whose time complexity is O(mn), where m and n are the number of links and nodes in the network, respectively. We present a novel integer programming formulation for the general VPN tree computation problem (that is, when ingress and egress bandwidths of VPN endpoints are arbitrary) and develop an algorithm that is based on the primal-dual method. Finally, we extend our proposed algorithms for computing VPN trees to the case when network links have capacity constraints. We show that in the presence of link capacity constraints, computing the optimal VPN tree is NP-hard even when ingress and egress bandwidths of each endpoint are equal. Our experimental results with synthetic network graphs indicate that the VPN trees constructed by our proposed algorithms dramatically reduce bandwidth requirements (in many instances, by more than a factor of 2) compared to scenarios in which Steiner trees are employed to connect VPN endpoints.

Consider a setting in which a group of nodes, situated in a large underlying network, wishes to r... more Consider a setting in which a group of nodes, situated in a large underlying network, wishes to reserve bandwidth on which to support communication. Virtual private networks (VPNs) are services that support such a construct; rather than building a new physical network on the group of nodes that must be connected, bandwidth in the underlying network is reserved for communication within the group, forming a virtual "sub-network."

Ans: A process for separating one or more metal ions forming a first group of metal ions such as ... more Ans: A process for separating one or more metal ions forming a first group of metal ions such as copper, zinc and ferric ions, from one or more other metal ions forming a second group of metal ions such as cobalt and nickel, comprising: contacting an aqueous solution comprising said first and second groups of metal ions with an organic solution comprising a phosphinic acid and a hydroxyoxime to extract one of said groups of metal ions into the organic phase, and separating the organic and aqueous phases.

We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {... more We consider the Connected Facility Location problem. We are given a graph G = (V, E) with costs {c e } on the edges, a set of facilities F ⊆ V , and a set of clients D ⊆ V . Facility i has a facility opening cost f i and client j has d j units of demand. We are also given a parameter M ≥ 1. A solution opens some facilities, say F , assigns each client j to an open facility i(j), and connects the open facilities by a Steiner tree T . The total cost incurred is i∈F f i + j∈D d j c i(j)j + M e∈T c e . We want a solution of minimum cost.

We give simple and easy-to-analyze randomized approximation algorithms for several well-studied N... more We give simple and easy-to-analyze randomized approximation algorithms for several well-studied NP-hard network design problems. Our algorithms improve over the previously best known approximation ratios. Our main results are the following.

Computer Communication Review, 2001

Virtual Private Networks (VPNs) provide customers with predictable and secure network connections... more Virtual Private Networks (VPNs) provide customers with predictable and secure network connections over a shared network. The recently proposed hose model for VPNs allows for greater flexibility since it permits traffic to and from a hose endpoint to be arbitrarily distributed to other endpoints. In this paper, we develop novel algorithms for provisioning VPNs in the hose model. We connect VPN endpoints using a tree structure and our algorithms attempt to optimize the total bandwidth reserved on edges of the VPN tree. We show that even for the simple scenario in which network links are assumed to have infinite capacity, the general problem of computing the optimal VPN tree is NP-hard. Fortunately, for the special case when the ingress and egress bandwidths for each VPN endpoint are equal, we can devise an algorithm for computing the optimal tree whose time complexity is O(mn), where m and n are the number of links and nodes in the network, respectively. We present a novel integer programming formulation for the general VPN tree computation problem (that is, when ingress and egress bandwidths of VPN endpoints are arbitrary) and develop an algorithm that is based on the primal-dual method. Finally, we extend our proposed algorithms for computing VPN trees to the case when network links have capacity constraints. We show that in the presence of link capacity constraints, computing the optimal VPN tree is NP-hard even when ingress and egress bandwidths of each endpoint are equal. Our experimental results with synthetic network graphs indicate that the VPN trees constructed by our proposed algorithms dramatically reduce bandwidth requirements (in many instances, by more than a factor of 2) compared to scenarios in which Steiner trees are employed to connect VPN endpoints.

Consider a setting in which a group of nodes, situated in a large underlying network, wishes to r... more Consider a setting in which a group of nodes, situated in a large underlying network, wishes to reserve bandwidth on which to support communication. Virtual private networks (VPNs) are services that support such a construct; rather than building a new physical network on the group of nodes that must be connected, bandwidth in the underlying network is reserved for communication within the group, forming a virtual "sub-network."

Ans: A process for separating one or more metal ions forming a first group of metal ions such as ... more Ans: A process for separating one or more metal ions forming a first group of metal ions such as copper, zinc and ferric ions, from one or more other metal ions forming a second group of metal ions such as cobalt and nickel, comprising: contacting an aqueous solution comprising said first and second groups of metal ions with an organic solution comprising a phosphinic acid and a hydroxyoxime to extract one of said groups of metal ions into the organic phase, and separating the organic and aqueous phases.