# Questions tagged [constraint-satisfaction]

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### What is Least-Constraining-Value?

In constraint satisfaction problems, heuristics can be used to improve the performance of a bactracking solver. Three commonly given heuristics for simple backtracking solvers are: Minimum-remaining-...
300 views

### Algorithm for solving planar constraint problem (“Pokemon Go monster finding”)

[Note: This problem was inspired by Pokemon Go. I will first explain the problem in mathematical terms, then explain the connection to Pokemon Go. My goal is not to cheat in the game. If I wanted to ...
215 views

1k views

### Contraint with three variables into three binary constraints

I'm having a hard time tackling the following problem (perhaps some key data is missing). We have a constraint: $A+B= C$ One is supposed to represent this one constraint using three binary ...
98 views

### Answer Set Program to SAT translation

During the presentation (a talk) Answer Set Programming: Boolean Constraint Solving for Knowledge Representation and Reasoning Torsten Schaub (University of Postdam) stated around twenty-one minutes ...
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### What is the generating algorithm for the “komb” instances found on satcompetition.org?

For the 2017 and 2018 Random SAT Tracks of the SAT Competition ran by the International Conference on Theory and Applications of Satisfiability Testing there are small, yet difficult, random 3-SAT ...
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### (Historical perspective) CSP and SAT inter-fertilization

[Disclaimer: this is a rather specialized question] It is known that techniques like Conflict-Driven Clause Learning (CDCL) and back-jumping -- which improved the Satisfiability (SAT) strategies ...
179 views

### Is every X3SAT instance with no cycles satisfiable?

Exactly 1 in 3 SAT (X3SAT) is a variation of the Boolean Satisfiability problem. Given a set of clauses, where each clause has three literals, is there an assignment such that in each clause exactly ...
78 views

### existence of a permutation that satisfies order-constraints

I would like to know if there is a simple algorithm for checking the existence of a permutation that satisfies a number of order-constraints. For example, suppose we have a set (1, 2, 3, 4, 5) and a ...
117 views

### Sum of unique integers to cnf constraint

As a study project I try to solve the kakuro puzzle problem using SAT SOLVER. I can't really find an efficient way to convert the sum of k unique integers (1...9) to a CNF constraint. What I had in ...
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### General structure of solutions to 3-SAT circuits

Certain special forms of the SAT problem have solution sets of a special form. For example, given any three solutions to a 2-SAT circuit, their bitwise median is also a solution. Likewise, given any ...
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### Theoretical CSPs where (in)equality constraints can be expressed as a single constraint?

I'm designing puzzles by running a MAX-CSP solver, and it works nicely in practice. For concreteness, my problems have the following form (in a pseudo-modeling language): ...
155 views

### Isn't Domain of a variable nothing but a constraint?

In Constraint programming we have Variables and their Domains and then all the constraints, but if you at the concept of a domain of a variable it is nothing but another type of constraint, you are ...
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### CSP Forward checking with n-ary (and binary) constraints

I have implemented my own CSP solver using a Backtracking algorithm. Within the Backtracking algorithm I apply a Forward Checking algorithm (reducing domains of connected, unnasigned variables) that ...
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### Linear optimization or Constraint Satisfaction Problem with food

I was hoping someone could point me in the right direction in terms of what type of problem I am describing here so I can research it. My initial thought is that it is some form of Constraint ...
69 views

### Proving NP hardness about graph creation problem with triangle number

I have graph creation problem. Given a set of nodes of graph, and node constraints such as given every node's number of neighbors (degree). I am also provided with the total number of triangles in ...
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### Given two arrays of length n and n - 1, order the first array such that no partial sum is in the second array

Two arrays of natural numbers are given of length $n$ and $n - 1$: e.g. $A: [a_0, a_1,..., a_{n-1}, a_n]$ $B: [b_0, b_1, ..., b_{n-2}, b_{n-1}]$ All elements of $A$ are unique (can be in $B$), all ...
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### Knowing if I have an optimal ordering for a OBDD

I'm learning about OBDD and I have learned that the size of a reduced OBDD (ROBDD) is dependent on the ordering of the variables, and that finding an optimal ordering is an NP hard problem. Say I ...
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### Constraint Satisfaction: maximizing total value with no overlaps

Suppose we have a bunch of bars, which can represent anything (time slots, paths, physical items...) and each of them has a start point, an end point, and an associated value. Out of all the bars ...
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### Linear programming over a finite field

I have a system of equations $Ax = b$ over some finite field $\mathbb{Z}_p$ and want to find a feasible solution. I'm sure this problem is NP-hard, but I'm struggling to find any literature on the ...
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### Binarization of Constraints

I am trying to solve a Constraint Satisfaction Problem that involves lots of n-ary constraints. But the solver I have implemented only works with algorithms for binary constraints. I've been reading ...
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### Are finite-domain binary constraint satisfaction problems solvable in polynomial time?

Suppose a CSP has $n$ variables with finite domains of maximal size $d$. Furthermore, all constraints on the variables are binary. Can such a CSP be solved in polynomial time in $n$ and $d$? This was ...
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### Need recursive version of Conflict based backjumping

I am implementing conflict directed Backjumping algorithm of prosser in java. But, the algorithm is iterative approach. How can it be built with recursive approach? In AIMA they give the recursive ...
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### IA network that is path-consistent, but not consistent

I'm studying continuous CSP from the slides of my professor and i got that with the PATH-CONSISTENCY algorithm you can check consistency for PA (Point Algebra), SIA and ORD-Horn; however it cannot be ...
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### Is there a “well known” example of a constraint satisfaction problem on a 3-element set which is polynomial-time solvable?

I'm basically looking for an example (in maybe graph theory) of a constraint satisfaction problem which has a 3-element set as a domain and the problem is known to be polynomial-time solvable.
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### Mimimum spanning tree with a constraint on number of certain types of edges

I have the the following problem. Say we have a graph $G = (V,E)$ where all $e \in E$ have positive weight, and $E$ can be separated in to two disjoint sets $E = A \cup B$. We have to find a spanning ...
530 views