Questions tagged [constraint-satisfaction]
The constraint-satisfaction tag has no usage guidance.
118
questions
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29 views
Routing with constraints
The following is the statement of the problem:
There are 40 packets to be delivered in a day. Each packet needs to be delivered to a
particular location. Apart from this, there are constraints also ...
2
votes
2answers
59 views
Efficient Algorithm to Find the Closest Integer Representation, in the Form $A\times\frac{N}{D}$ for a Value
The Problem
I am working on a problem that boils down to finding the closest representation of an arbitrary number ($x$) in the form:
$$x = A\times\frac{N}{D}$$
Where $A$ is a 32-bit integer, and $N$ ...
1
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1answer
72 views
Are there any solvers that can handle non-linearity?
I need a way to solve linear and non-linear inequalities over the natural numbers. So equations like this should be solveable:
$\forall n, p, q \in \mathbb{N}. q \cdot (1 + n^p) \leq q$
From what I ...
0
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1answer
63 views
Non-convex linear program optimisation with infinite number of OR constraints
I am aware that when we have a linear problem subject to OR constraints, the LP would be a non-convex optimisation problem. For example,
${x = 0}$ OR ${1<=x<=2}$.
My question is in such a ...
0
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2answers
29 views
Is the following problem NP-Complete? [closed]
3SAT with the additional condition that exactly 1 or 3 literals must evaluate to 1.
0
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1answer
34 views
Solving a CSP using AC-3
Peter (P), Mary (M), Otto (O) and Dicky (D) would like to rent an apartment house. The house has three floors: G/F, 1/F, 2/F. Every floor has only one apartment. P, M, O and D must be assigned to ...
1
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2answers
25 views
Are joins/pullbacks of bloom filters possible?
An interesting advantage of bloom filters over hash tables, that they share with bitarrays, is that they support taking unions & intersections of sets by simply doing bitwise or & bitwise and ...
2
votes
1answer
26 views
Is there an optimization algorithm that could help match the maximum number clients to servers with constraints?
How do you go about solving the following problem that tries to match the greatest number of clients with servers with constraints? I'm trying to identify an algorithm or simulation that could help me ...
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0answers
41 views
QuickSort when the range of data is known
In QuickSort Algorithm, the pivot is chosen as the first element or a randomised element. However, if the range of data to be sorted is known, For example, from 1 to 100, and they are mostly equally ...
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1answer
26 views
would complexity of constraint satisfaction problem bound the constrained optimization problem?
If a constraint satisfaction problem $x \in Y$ is NP-Complete.
Can I conclude that the optimization problem $𝑥^* =\text{argmax}_x 𝑓(x)$ s.t. $x \in Y$ is also NP-Complete?
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27 views
would complexity of constrained optimization problem bound the constraint satisfaction problem?
For an optimization problem $x^* =\text{argmax}_xf(x)$ s.t. $x \in Y$ satisfy to some constraint $Y$.
Can I argue that if there is a polynomial algorithm for this optimization problem. Then there must ...
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105 views
Constraint based analysis: understanding the program $[[ \text{fn} \ x => [x]^1]^2 [ \text{fn} \ y => [y]^3]^4]^5$
I am currently studying the textbook Principles of Program Analysis by Flemming Nielson, Hanne R. Nielson, and Chris Hankin. Chapter 1.4 Constraint Based Analysis says the following:
1.4 Constraint ...
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0answers
29 views
IP Programming - objective function ist not a function BUT a table
Here is a short description of my problem:
Part of my objective function is not a regular function. Instead it's a table.
You can see a short extract here:
So if the height is smaller or equal to 300 ...
2
votes
2answers
77 views
Constraint satisfaction problem: solve system, then evaluate whether many additional constraints are satisfied one at a time
I have a system that consists of binary inequality constraints between variables, plus some indicator variables that can assume only two values:
...
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79 views
How AC-3 (Arc Consistency) with backtracking works
I'm trying to understand the AC-3 algorithm with backtracking to implement a Rat in Maze algorithm via C++. So far I've base on these links I have a basic idea in terms of AC-3 and how to implement ...
0
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1answer
35 views
Generating topological sequence from DAG with additional "not appearing before" constraints
DAG specifies the relationship of one node must appear after another. What if I add an additional constraint where one node cannot appear before another on top of the DAG?
Is there an algorithm for ...
4
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0answers
104 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 ...
1
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2answers
195 views
Automated reasoning with real numbers
I have a large number of equivalences which look like:
$(a \leq 0.54 \wedge b \geq 0.12) \vee (c \gt 0.98)$ $\Leftrightarrow$ $(x \leq 0.25) \vee (x \gt 0.91 \wedge y \geq 0.01)$
This is just an ...
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0answers
33 views
Can arc consistency checks be avoided if constraints are formulated properly?
While solving a few CSPs by hand, I noticed that I don't actually need to check for arc consistency after each assignment.
All I needed to do was to formulate the CSP in such a way that I'm adding ...
2
votes
1answer
38 views
CSP heuristics to help avoid redundancy while checking values for constraint inconsistency?
I'm a complete beginner. Please forgive my ignorance.Trying to learn about CSP online, I noticed a lot of the focus on search methods and heuristics which tell you which variable to expand next (e.g. ...
2
votes
1answer
119 views
How can we formulate an anti-knight Sudoku as an exact cover problem?
Formulating standard Sudoku as an exact cover problem is easy and well documented. All of the constrained groups contain every digit which makes it natural to express the problem this way. Wikipedia ...
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3answers
185 views
Counting the number of satisfied models - given mathematical constraints
Question
There are plenty of algorithms for solving the #SAT problem, with one being the DPLL algorithm and is implemented for all kinds of programming languages. As far as I've seen, they all take a ...
2
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1answer
62 views
How to represent sums of piecewise quadratic functions for efficient optimisation?
I'm trying to implement a decision procedure for finding solutions to a scheduling problem; this involves computing the point in time which is under the most contention. Each task to be scheduled has ...
1
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2answers
58 views
Algorithm for optimal rule-based arrangements?
I am trying to plant a row in a garden. Certain plants are good for some plants and bad for others, and I am trying to find the best order of plants: most adjacent friends and no adjacent foes, as ...
1
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2answers
32 views
Algebra for min/max bounds
I am trying to model some set operations which are only well-defined if one is a subset of the other. The way the sets are constructed, I'll have a series of constraints of the form $x \subseteq y$, ...
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69 views
Special case of stable marriage
I have an instance of the stable marriage problem in which the first side $S_1$ has $n_1$ agents and the second side $S_2$ has $n_2$ agents with $n_2$ is very big in comparison to $n_1$. In addition, ...
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19 views
How to change the constraint's arity from n to 3?
How to change the constraint's arity from n to 3?
I know how to perform binarization of constraints, explained here: https://cw.fel.cvut.cz/b172/_media/courses/b4b36zui/binarization.pdf, but I don't ...
2
votes
1answer
121 views
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 ...
6
votes
1answer
2k views
Algorithm to create dense style crossword puzzles
I am working on creating a program to generate dense American style crossword puzzles of grid sizes between 15x15 - 30x30. The database of words I'm using ranges between 20,000 and 100,000 words of ...
1
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1answer
18 views
Equivalence between MIN UNCUT and MIN-CSP_XOR
In this paper
Agarwal, Amit, et al. "O (√ log n) approximation algorithms for min UnCut, min 2CNF deletion, and directed cut problems." Proceedings of the thirty-seventh annual ACM symposium on ...
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0answers
23 views
Repair operator for evolutionary algorithm
I am working on a resource allocation problem using an SPEA 2 evolutionary algorithm. The problem involves decision variables where each variable has a different domain e.g. $E_i \le d_i$ where $E_i$ ...
1
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1answer
48 views
Multi-Path Length Minimization
I've been thinking about path planning and am trying to make good heuristics for cases with multiple agents.
Suppose there are sets $S_i$ of coordinates in $\mathbb R^2$ or $\mathbb R^3$, each of the ...
0
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1answer
47 views
Why N-Queens Problem is not used as experiment in CSP thesis?
I am studying CSP for my master thesis. I found that many thesis based on CSP described N-Queens as an introductory and they actually do experiment on random CSP problems.
If so,when I do master ...
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0answers
27 views
Find an algorithm to fully consume items with criteria and produce minimal result
So here are the prerequisites:
There are items to be consumed. Consider an item is just an object with a bunch of properties (e.g. size, weight), and there are tens or hundreds of properties.
Items ...
1
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1answer
84 views
Selection over combinatorics that satisfies a distribution
I'm having an exciting problem that I could not manage to find an optimized solution. I actually have no idea if the problem is already known or not.
Here is the problem :
Consider a list of M ...
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1answer
25 views
Bin Packing variant
I am currently struggling with a bin packing variant, where we have fuel and compartments of a tank truck. Some industry constraints apply, but the whole picture is that you must fit the total volume ...
2
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1answer
96 views
Mutli-Path Collision Avoidance
I need an algorithm which can do the following:
Given some finite number of particles (circles) each with the same radius, and a list of prescribed points for each particle, find paths in $\mathbb{...
2
votes
2answers
132 views
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 ...
2
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0answers
189 views
Least constraining value heuristic in Sudoku [closed]
I was trying to implement Least Constraining Value Heuristic in Sudoku but wasn't getting the idea on how to do it. Can someone share their idea for the same ?
2
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1answer
56 views
Non-Boolean SAT
I was wondering about the complexity of SAT tests with variables $x_i = 0 \lor 1 \lor 2 \dots \lor n$, with clauses being of the form $x_i = a \implies x_j \neq b$. When $n=2$, we have 2SAT, which has ...
1
vote
1answer
63 views
Can an optimization algorithm be "universal"?
I am wondering if a Bayesian Optimization framework (e.g. Google's Vizier) can be used in lieu of a traditional solver like Gurobi or CPLEX.
In trying to answer this question, I realized that I don'...
0
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1answer
196 views
"Greater than AND smaller than" condition in integer linear program with a binary variable
I found this related question, but that's not quite it
Is it possible to model this with integer programming:
$$A = \begin{cases} 1 & \text{if } B \geq C \geq D \\ 0 & \text{otherwise}\end{...
3
votes
1answer
138 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 ...
1
vote
1answer
20 views
Constraint propagation using Projection rule
I've found this example of constraint propagation using projection rule
We have
C = { x1 ≠ x2, x1 ≥ x2 }
< C; x1 ∈ {1,2,3}, x2 ∈ {1,2,3} >
They say that ...
7
votes
2answers
597 views
SAT algorithm for determining if a graph is disjoint
What are some good algorithms to have a SAT (CNF) solver determine if a given graph is fully-connected or disjoint?
The best one I can think of is this:
Number the nodes 1..N, where N is the number ...
4
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0answers
100 views
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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1answer
29 views
How to put elements in allowed bags?
Let's say I have a list of "Items"
I also have a list of "Bags". Each bag is a set of "Items" which gives what item can be placed in that bag. But only one item can go in each bag.
I want to place ...
1
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1answer
93 views
What is the time complexity of FC_MRV algorithm?
I am studying CSP and read the papers on it.I wanted to know the time complexity of Forward checking with Minium Remaining Value algorithm.
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38 views
Channeling Constraints in Constraint Handling Rules (CHR)
Suppose we have a constraint satisfaction problem that can be defined as its constraints in two different viewpoints $V_1$ and $V_2$. Moreover, there are two variables $A$ and $B$ from $V_1$ and $V_2$ ...
1
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1answer
30 views
How to calculate the number of invalid strings given a constraint system on alphabet, word blacklist, and string length
If I have the following system, I am wondering how to calculate the number of valid strings it contains.
The system is something like this, which can have arbitrary variations.
Only consists of an ...
