10 research outputs found
The Combined Basic LP and Affine IP Relaxation for Promise VCSPs on Infinite 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\u2720] for promise (non-valued) CSPs (on finite domains)
The combined basic LP and affine IP relaxation for promise VCSPs on infinite 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).Comment: Full version of an MFCS'20 pape
Algebraic Approach to Approximation
Following the success of the so-called algebraic approach to the study of
decision constraint satisfaction problems (CSPs), exact optimization of valued
CSPs, and most recently promise CSPs, we propose an algebraic framework for
valued promise CSPs.
To every valued promise CSP we associate an algebraic object, its so-called
valued minion. Our main result shows that the existence of a homomorphism
between the associated valued minions implies a polynomial-time reduction
between the original CSPs. We also show that this general reduction theorem
includes important inapproximability results, for instance, the
inapproximability of almost solvable systems of linear equations beyond the
random assignment threshold
The combined basic LP and affine IP relaxation for promise VCSPs on infinite 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)
The combined basic LP and affine IP relaxation for promise VCSPs on infinite 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)