Esha Ghosh

Faster parameterized algorithms for deletion to split graphs

An undirected graph is said to be split if its vertex set can be partitioned into two sets such that the subgraph induced on one of them is a complete graph and the subgraph induced on the other is an independent set. We study the problem of deleting the minimum number of vertices or edges from a given input graph so that the resulting graph is split.We initiate a systematic study and give efficient fixed-parameter algorithms and polynomial sized kernels for the problem. More precisely, 1 for Split Vertex Deletion, the problem of determining whether there are k vertices whose deletion results in a split graph, we give an

Hash First, Argue Later: Adaptive Verifiable Computations on Outsourced Data

{\cal O}^*(2^k)

Zero-Knowledge Authenticated Order Queries and Order Statistics on a List

algorithm improving on the previous best bound of

Efficient Verifiable Range and Closest Point Queries in Zero-Knowledge

{\cal O}^*({2.32^k})

Verifiable Zero-Knowledge Order Queries and Updates for Fully Dynamic Lists and Trees

. We also give an

Zero-Knowledge Accumulators and Set Algebra

{\cal O}(k^3)

A polynomial time algorithm for longest paths in biconvex graphs

-sized kernel for the problem. 2 For Split Edge Deletion, the problem of determining whether there are k edges whose deletion results in a split graph, we give an

Faster Parameterized Algorithms for Deletion to Split Graphs

{\cal O}^*( 2^{ O(\sqrt{k}\log k) })

Verifiable Member and Order Queries on a List in Zero-Knowledge.

algorithm. We also prove the existence of an

Zero-Knowledge Accumulators and Set Operations

{\cal O}(k^2)