scholarly journals The Combined Basic LP and Affine IP Relaxation for Promise VCSPs on Infinite Domains

2021 ◽  
Vol 17 (3) ◽  
pp. 1-23
Author(s):  
Caterina Viola ◽  
Christian Coester
Keyword(s):  
Linear Programming ◽  
Integer Programming ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Sufficient Condition ◽  
Convex Relaxations ◽  
Infinite Domain ◽  
Exact Solvability ◽  
Infinite Domains ◽  
Finite Domains

Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most recently promise CSPs. In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming relaxation for exact solvability of promise valued CSPs over infinite-domains. This extends a result of Brakensiek and Guruswami (SODA’20) for promise (non-valued) CSPs (on finite domains).

SHARED MEMORY IMPLEMENTATION OF CONSTRAINT SATISFACTION PROBLEM RESOLUTION

2001 ◽  
Vol 11 (04) ◽  
pp. 487-501 ◽  
Author(s):  
ZINEB HABBAS ◽  
MICHAËL KRAJECKI ◽  
DANIEL SINGER
Keyword(s):  
Load Balancing ◽  
Shared Memory ◽  
Constraint Satisfaction ◽  
Parallel Implementation ◽  
Constraint Satisfaction Problem ◽  
Search Tree ◽  
Constraint Satisfaction Problems ◽  
Memory Model ◽  
Problem Resolution ◽  
Finite Domains

Many problems in Computer Science, especially in Artificial Intelligence, can be formulated as Constraint Satisfaction Problems (CSP). This paper presents a parallel implementation of the Forward-Checking algorithm for solving a binary CSP over finite domains. Its main contribution is to use a simple decomposition strategy in order to distribute dynamically the search tree among machines. The feasibility and benefit of this approach are studied for a Shared Memory model. An implementation is drafted using the new emergent standard OpenMP library for shared memory, thus controlling load balancing. We mainly highlight satisfactory efficiencies without using any tricky load balancing policy. All the experiments were carried out running on the Sillicon Graphics Origin 2000 parallel machine.

scholarly journals The Power of the Combined Basic Linear Programming and Affine Relaxation for Promise Constraint Satisfaction Problems

2020 ◽  
Vol 49 (6) ◽  
pp. 1232-1248
Author(s):  
Joshua Brakensiek ◽  
Venkatesan Guruswami ◽  
Marcin Wrochna ◽  
Stanislav Živný
Keyword(s):  
Linear Programming ◽  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems

scholarly journals Fine-Grained Time Complexity of Constraint Satisfaction Problems

2021 ◽  
Vol 13 (1) ◽  
pp. 1-32
Author(s):  
Peter Jonsson ◽  
Victor Lagerkvist ◽  
Biman Roy
Keyword(s):  
Constraint Satisfaction ◽  
Time Complexity ◽  
Constraint Satisfaction Problem ◽  
Constraint Satisfaction Problems ◽  
Finite Domain ◽  
Infinite Domain ◽  
Worst Case ◽  
Fine Grained ◽  
Restricted Problems ◽  
Np Complete

We study the constraint satisfaction problem (CSP) parameterized by a constraint language Γ (CSPΓ) and how the choice of Γ affects its worst-case time complexity. Under the exponential-time hypothesis (ETH), we rule out the existence of subexponential algorithms for finite-domain NP-complete CSPΓ problems. This extends to certain infinite-domain CSPs and structurally restricted problems. For CSPs with finite domain D and where all unary relations are available, we identify a relation S D such that the time complexity of the NP-complete problem CSP({ S D }) is a lower bound for all NP-complete CSPs of this kind. We also prove that the time complexity of CSP({ S D }) strictly decreases when |D| increases (unless the ETH is false) and provide stronger complexity results in the special case when |D|=3.

scholarly journals The Complexity of Promise SAT on Non-Boolean Domains

2021 ◽  
Vol 13 (4) ◽  
pp. 1-20
Author(s):  
Alex Brandts ◽  
Marcin Wrochna ◽  
Stanislav Živný
Keyword(s):  
Polynomial Time ◽  
Constraint Satisfaction ◽  
Algebraic Approach ◽  
Constraint Satisfaction Problems ◽  
Hardness Of Approximation ◽  
Np Hard ◽  
Cover Problem ◽  
Finite Domains ◽  
Np Hardness ◽  
Cnf Formulas

While 3-SAT is NP-hard, 2-SAT is solvable in polynomial time. Austrin et al. [SICOMP’17] proved a result known as “(2+ɛ)-SAT is NP-hard.” They showed that the problem of distinguishing k -CNF formulas that are g -satisfiable (i.e., some assignment satisfies at least g literals in every clause) from those that are not even 1-satisfiable is NP-hard if g/k < 1/2 and is in P otherwise. We study a generalisation of SAT on arbitrary finite domains, with clauses that are disjunctions of unary constraints, and establish analogous behaviour. Thus, we give a dichotomy for a natural fragment of promise constraint satisfaction problems ( PCSPs ) on arbitrary finite domains. The hardness side is proved using the algebraic approach via a new general NP-hardness criterion on polymorphisms, which is based on a gap version of the Layered Label Cover problem. We show that previously used criteria are insufficient—the problem hence gives an interesting benchmark of algebraic techniques for proving hardness of approximation in problems such as PCSPs.

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