Raising NP lower bounds to parallel NP lower bounds

Some Open Problems regarding Lower Bounds for Np

This issue’s Open Problem Column is by Ryan Williams and is on Some Open Problems Regarding Lower Bounds For NP. Ryan himself has made progress on lower bounds for SAT and is an expert in the area. I invite any reader who has knowledge of some area to contact me and arrange to write a column about open problems in that area. That area can be (1) broad or narrow or anywhere inbetween, and (2) re...

Some Lower Bounds for Estrada Index

CMSC 858 F : Algorithmic Lower Bounds Fall 2014 3 - SAT and NP - Hardness

The most important NP-Complete (logic) problem family!

P != NP, propositional proof complexity, and resolution lower bounds for the weak pigeonhole principle

Recent results established exponential lower bounds for the length of any Resolution proof for the weak pigeonhole principle. More formally, it was proved that any Resolution proof for the weak pigeonhole principle, with n holes and any number of pigeons, is of length fl(2 ), (for a constant e = 1/3). One corollary is that certain propositional formulations of the statement P / NP do not have s...

Parameterized Lower Bounds and Dichotomy Results for the NP-completeness of H-free Edge Modification Problems

For a graph H, the H-free Edge Deletion problem asks whether there exist at most k edges whose deletion from the input graph G results in a graph without any induced copy of H. H-free Edge Completion and H-free Edge Editing are defined similarly where only completion (addition) of edges are allowed in the former and both completion and deletion are allowed in the latter. We completely settle th...