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- Joseph Cheriyan, Ramakrishna Thurimella
- SIAM J. Comput.
- 1996

Abstract An e cient heuristic is presented for the problem of nding a minimum size k connected spanning subgraph of an undirected or directed simple graph G V E There are four versions of the problem and the approximation guarantees are as followsAn e cient heuristic is presented for the problem of nding a minimum size k connected spanning subgraph of an… (More)

- Joseph Cheriyan, S. N. Maheshwari
- J. Algorithms
- 1988

- Joseph Cheriyan, Ming-Yang Kao, Ramakrishna Thurimella
- SIAM J. Comput.
- 1993

- F. Sibel Salman, Joseph Cheriyan, R. Ravi, S. Subramanian
- SODA
- 1997

1 Introduction. We initiate the algorithmic study of an important but NP-hard problem that arises commonly in network design. The input consists of (1) An undirected graph with one sink node and multiple source nodes, a specified length for each edge, and a specified demand, dem,, for each source node v. (2) A small set of cable types, where each cable type… (More)

- Joseph Cheriyan, Mohammad R. Salavatipour
- APPROX-RANDOM
- 2005

Given an undirected graph <i>G</i>(<i>V</i>, <i>E</i>) with terminal set <i>T</i> ⊆ <i>V</i>, the problem of packing element-disjoint Steiner trees is to find the maximum number of Steiner trees that are disjoint on the nonterminal nodes and on the edges. The problem is known to be NP-hard to approximate within a factor of Ω(log <i>n</i>), where… (More)

- Joseph Cheriyan, Howard J. Karloff, Yuval Rabani
- FOCS
- 2001

The seminal paper of Leighton and Rao (1988) and subsequent papers presented approximate minmax theorems relating multicommodity flow values and cut capacities in undirected networks, developed the divide-and-conquer method for designing approximation algorithms, and generated novel tools for utilizing linear programming relaxations. Yet, despite persistent… (More)

- Joseph Cheriyan, Adrian Vetta
- STOC
- 2005

We study undirected networks with edge costs that satisfy the triangle inequality. Let <i>n</i> denote the number of nodes. We present an <i>O</i>(1)-approximation algorithm for a generalization of the metric-cost subset <i>k</i>-node-connectivity problem. Our approximation guarantee is proved via lower bounds that apply to the simple edge-connectivity… (More)

- Joseph Cheriyan, Ramakrishna Thurimella
- J. Algorithms
- 1996

A k-separator (k-shredder) of a graph is a set of k nodes whose removal results in two or more (three or more) cunnect ed components. Let the given (undirected) graph be k-node connected, and let n denote the number of nodes. Solving au open question, we show that the problem of counting the number of k-separators is #P-complete. However, we present an… (More)

- Joseph Cheriyan, Santosh Vempala, Adrian Vetta
- SIAM J. Comput.
- 2003

We present an approximation algorithm for the problem of finding a minimum-cost k-vertex connected spanning subgraph, assuming that the number of vertices is at least 6k. The approximation guarantee is six times the kth harmonic number (which is O(log k)), and this is also an upper bound on the integrality ratio for a standard linear programming relaxation.

- Joseph Cheriyan, Santosh Vempala, Adrian Vetta
- Combinatorica
- 2006

A typical problem in network design is to nd a minimum-cost sub-network H of a given network G such that H satisses some prespeciied connectivity requirements. Our focus is on approximation algorithms for designing networks that satisfy vertex connectivity requirements. Our main tool is a linear programming relaxation of the following setpair formulation… (More)