Computational complexity continuum within Ising formulation of NP problems

Ising formulations of many NP problems

*Correspondence: Andrew Lucas, Lyman Laboratory of Physics, Department of Physics, Harvard University, 17 Oxford St., Cambridge, MA 02138, USA e-mail: [email protected] We provide Ising formulations for many NP-complete and NP-hard problems, including all of Karp’s 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering, and satisfiability....

Computational Complexity of Discrete Problems

This report documents the program and the outcomes of Dagstuhl Seminar 17121 “Computational Complexity of Discrete Problems”. The first section gives an overview of the topics covered and the organization of the meeting. Section 2 lists the talks given in alphabetical order. The last section contains the abstracts of the talks. Seminar March 19–24, 2017 – http://www.dagstuhl.de/17121 1998 ACM S...

Computational Complexity of Continuous Problems

Computational Complexity of Holant Problems

We propose and explore a novel alternative framework to study the complexity of counting problems, called Holant problems. Compared to counting constraint satisfaction problems (#CSP), it is a refinement with a more explicit role for the constraint functions. Both graph homomorphism and #CSP can be viewed as special cases of Holant problems. We prove complexity dichotomy theorems in this framew...

Computational Complexity of Dynamic Problems

This progress report surveys some of my scientiic work on part A of the Ph.D.-programme at the Computer Science Department of the University of Aarhus. I give a survey-like introduction to the eld of Complexity Theory to which my results bear relevance. I give a general account of my contributions to the eld, including the the Dynamic Transitive Closure Problem for spherical st-graphs, the Dyna...