Description du projet
Des algorithmes de temps exponentiel plus efficaces pour calculer les solutions aux problèmes NP-complets
L’algorithme P versus NP est un problème informatique majeur qui demeure non résolu. Il cherche à savoir si chaque problème dont la solution peut être vérifiée rapidement (temps polynomial) peut aussi être résolu rapidement (en temps polynomial également). Jusqu’à présent, peu de progrès ont été enregistrés en ce qui concerne la découverte d’algorithmes qui améliorent grandement les temps d’exécution. Le projet CRACKNP, financé par l’UE, entend s’attaquer au cœur de ce problème en concevant la prochaine génération d’algorithmes de temps exponentiel exact. Afin de développer ces algorithmes, le projet cherchera à apporter une réponse aux problèmes NP-complets les plus connus (dont les solutions peuvent être vérifiées en temps polynomial). Il traitera également le problème du voyageur de commerce, le problème de satisfaisabilité en forme normale conjonctive et le problème du sac à dos.
Objectif
Assuming P does not equal NP, there are no polynomial time algorithms for any NP-complete problem. This however still leaves a huge gap between anything super-polynomial and the exponential run times of trivial exhaustive search. The study of exact (exponential time) algorithms that aims to breach this gap is as old as Theoretical Computer Science (TCS) itself: Already in the 1960's, researchers found elementary (for modern standards) algorithms that greatly improve exponential the run times. But over time, TCS seems to have hit a brick wall: Somewhat embarrassingly, as of 2018 the run times of these classic algorithms are still the best known for many classic problems.
This project aims to strike at the heart of this issue by designing the next generation of exact exponential time algorithms. To obtain these algorithms, we consider the most famous NP-complete problems such as Traveling Salesman, CNF-Sat and Knapsack, and we challenge ourselves to improve the classic currently best algorithms for them. These problems have served as a prototypical test bed for many algorithmic techniques with extensive applications, and thus their study provides an excellent road map towards our aim.
Moreover, in the last few years it was shown that these algorithms have consequences that reach much further than originally thought: In particular, they would have a major impact on research in polynomial time algorithms, circuit complexity and parameterized complexity.
Now is the right moment for this project, as recent work (partially by the PI) has given a first glimpse of a new algorithmic toolkit emerging: Advanced new tools to decompose solutions such as the representation method, the rank-based method and the polynomial method, are still barely exploited and studied in the field.
In this project we will combine these (and many more) tools in novel ways that transcend existing approaches, and make cracks in the wall of NP-completeness seem entirely within reach.
Mots‑clés
Programme(s)
Thème(s)
Appel à propositions
(s’ouvre dans une nouvelle fenêtre) ERC-2019-STG
Voir d’autres projets de cet appelRégime de financement
ERC-STG - Starting GrantInstitution d’accueil
3584 CS Utrecht
Pays-Bas