Faster algorithms for weak backdoors
WebWe explore the semantics of strong backdoors in satisable instances and their relation to counting solutions. In partic-ular, while pure literal backdoors only facilitate the decision of satisability , strong backdoors w.r.t. unit propagation are also backdoors for the problem of counting solutions. 2 Preliminaries and Related Work WebThe main results are positive: (1) There is a cubic-time algorithm that, given a CNF formula F and two constants k,t\ge 0, either finds a strong W_t-backdoor set of size at most 2^k, …
Faster algorithms for weak backdoors
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Webbackdoors, which is essential for studying value and variable ordering mistakes. I discuss our definition of sub-solvers and propose algorithms for finding backdoors. I implement our proposed algorithms by modifying a state-of-the-art SAT solver, Min-isat. I analyze experimental results comparing our proposed algorithms to previous WebThese results include (omitting polynomial factors), (i) a 4.54 k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Horn formulas; (ii) a 2.27 k algorithm to detect whether there is a weak backdoor set of at most k variables into the class of Krom formulas.
Webformula the minimum size of a weak backdoor does not exceed the size of a strong one. However, this is not true for unsatisfiable formulas. For example, any unsatisfiable … WebJun 28, 2024 · A weak backdoor, or simply a backdoor, for a Boolean SAT formula F into a class of SAT formulae C is a partial truth assignment T such that F[T] is in C and satisfiability is preserved. The problem of finding a backdoor from class C1 into class C2, or …
WebAug 23, 2024 · For “traditional” types of backdoors (i.e. strong and weak backdoors ), if the backdoor is small, then efficient algorithms can determine satisfiability by trying all possible assignments to the backdoor. Unfortunately, traditional backdoors do not account for some pivotal aspects of CDCL SAT solvers, such as clause-learning or restarts. Webweak backdoor (there exists an instantiation of the backdoor variables that produces a satisfiable instance that belongs to C) and a strong backdoor (all instantiations for the backdoor variables result in an instance that belongs to C). This paper shall focus on strong backdoors since weak backdoors exist only for satisfiable formulas.
WebThe Shortest Path Faster Algorithm (SPFA) is an improvement of the Bellman–Ford algorithm which computes single-source shortest paths in a weighted directed graph. …
Webclauses. We will say that a weak backdoor assignment from class C 1 to C 2 for a formula ˚∈C 1 is a truth assignment ˝: S→{true;false}to a subset of variables S⊆Var(˚) such that … hot breath of the wild zeldaWebfind that such instances often have backdoors involving under 5% of the dis-crete variables. Interestingly, sometimes the optimality-proof backdoors can in fact be smaller … hot breaking newsWebWe propose FPT approximation algorithms to compute backdoor depth into the classes ... heuristic algorithms work surprisingly fast on real-world CnfSat instances [9]. A common expla- ... 1We focus on strong backdoors; we will not consider weak backdoors as they only apply to satis able formulas. 1 arXiv:2202.08326v1 [cs.DS] 16 Feb 2024 ... psychrometer readingWebJun 10, 2024 · Abstract. We propose a machine learning approach for quickly solving Mixed Integer Programs (MIPs) by learning to prioritize sets of branching variables at the root node which result in faster solution times, which we call pseudo-backdoors. Learning-based approaches have seen success in combinatorial optimization by flexibly leveraging … psychrometer measureWebnatorial problems to allow faster algorithms than for general unstructured or random instances. For SAT and its counting version #SAT, hidden structure has been exploited … hot breath when sickWebfind that such instances often have backdoors involving under 5% of the dis-crete variables. Interestingly, sometimes the optimality-proof backdoors can in fact be smaller than the weak optimality backdoors, and this aligns with the relative runtime distributions for these problems when finding an optimal solu-tion vs. when proving optimality. hot breed monster crownWebFaster Algorithms for Weak Backdoors. ... Separate, Measure and Conquer: Faster Algorithms for Max 2-CSP and Counting Dominating Sets. ICALP 2015: Proceedings of … psychrometer what does it do