Iterative compression and exact algorithms

Iterative Compression and Exact Algorithms

Iterative Compression has recently led to a number of breakthroughs in parameterized complexity. Here, we show that the technique can also be useful in the design of exact exponential time algorithms to solve NP-hard problems. We exemplify our findings with algorithms for the Maximum Independent Set problem, a parameterized and a counting version of d-Hitting Set and the Maximum Induced Cluster...

10. Iterative Compression - COMP6741: Parameterized and Exact Computation

Heuristic and exact algorithms for Generalized Bin Covering Problem

In this paper, we study the Generalized Bin Covering problem. For this problem an exact algorithm is introduced which can nd optimal solution for small scale instances. To nd a solution near optimal for large scale instances, a heuristic algorithm has been proposed. By computational experiments, the eciency of the heuristic algorithm is assessed.

Efficient and exact quantum compression

We present a divide and conquer based algorithm for optimal quantum compression / decompression, using O(n(log n) log log n) elementary quantum operations . Our result provides the first quasi-linear time algorithm for asymptotically optimal (in size and fidelity) quantum compression and decompression. We also outline the quantum gate array model to bring about this compression in a quantum com...

Connectivity Preserving Iterative Compression

When applying iterative compression to solve an optimization problem, we construct a smaller auxiliary graph from the input graph, solve the problem on this smaller graph, and then use the solution to solve the original problem. We present a variant of this approach in which the smaller graph inherits the connectivity properties of the original graph. This is especially useful when trying to so...