# Kanthi K. Sarpatwar

## Contact Details

NameKanthi K. Sarpatwar |
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## Pub CategoriesComputer Science - Data Structures and Algorithms (3) Computer Science - Discrete Mathematics (2) Computer Science - Computational Complexity (1) |

## Publications Authored By Kanthi K. Sarpatwar

We present a combinatorial algorithm that improves the best known approximation ratio for monotone submodular maximization under a knapsack and a matroid constraint to $\frac{1 -e^{-2}}{2}$. This classic problem is known to be hard to approximate within factor better than $1 - 1/e$. We show that the algorithm can be extended to yield a ratio of $\frac{1 - e^{-(k+1)}}{k+1}$ for the problem with a single knapsack and the intersection of $k$ matroid constraints, for any fixed $k > 1$. Read More

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph G[S] is connected. We present the first non-trivial \Omega(1/log n) approximation algorithm for the connected maximum cut problem in general graphs using novel techniques. We then extend our algorithm to an edge weighted case and obtain a poly-logarithmic approximation algorithm. Read More

We study partial and budgeted versions of the well studied connected dominating set problem. In the partial connected dominating set problem, we are given an undirected graph G = (V,E) and an integer n', and the goal is to find a minimum subset of vertices that induces a connected subgraph of G and dominates at least n' vertices. We obtain the first polynomial time algorithm with an O(\ln \Delta) approximation factor for this problem, thereby significantly extending the results of Guha and Khuller (Algorithmica, Vol. Read More

A path in an edge colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge colored graph is (strongly) rainbow connected if there exists a (geodesic) rainbow path between every pair of vertices. The (strong) rainbow connectivity of a graph G, denoted by (src(G), respectively) rc(G) is the smallest number of colors required to edge color the graph such that G is (strongly) rainbow connected. Read More