HyperBench

2021 ◽  
Vol 26 ◽  
pp. 1-40
Author(s):  
Wolfgang Fischl ◽  
Georg Gottlob ◽  
Davide Mario Longo ◽  
Reinhard Pichler
Keyword(s):  
Constraint Satisfaction ◽  
Decomposition Methods ◽  
Constraint Satisfaction Problems ◽  
Large Set ◽  
Web Interface ◽  
Conjunctive Queries ◽  
Practical Algorithms ◽  
New Infrastructure

To cope with the intractability of answering Conjunctive Queries (CQs) and solving Constraint Satisfaction Problems (CSPs), several notions of hypergraph decompositions have been proposed—giving rise to different notions of width, noticeably, plain, generalized, and fractional hypertree width (hw, ghw, and fhw). Given the increasing interest in using such decomposition methods in practice, a publicly accessible repository of decomposition software, as well as a large set of benchmarks, and a web-accessible workbench for inserting, analyzing, and retrieving hypergraphs are called for. We address this need by providing (i) concrete implementations of hypergraph decompositions (including new practical algorithms), (ii) a new, comprehensive benchmark of hypergraphs stemming from disparate CQ and CSP collections, and (iii) HyperBench, our new web-interface for accessing the benchmark and the results of our analyses. In addition, we describe a number of actual experiments we carried out with this new infrastructure.

scholarly journals Complexity Analysis of Generalized and Fractional Hypertree Decompositions

2021 ◽  
Vol 68 (5) ◽  
pp. 1-50
Author(s):  
Georg Gottlob ◽  
Matthias Lanzinger ◽  
Reinhard Pichler ◽  
Igor Razgon
Keyword(s):  
Polynomial Time ◽  
Constraint Satisfaction ◽  
Open Problem ◽  
Complexity Analysis ◽  
Decomposition Methods ◽  
Constraint Satisfaction Problems ◽  
Conjunctive Queries ◽  
Np Completeness ◽  
Np Complete ◽  
Efficient Approximation

Hypertree decompositions (HDs), as well as the more powerful generalized hypertree decompositions (GHDs), and the yet more general fractional hypertree decompositions (FHDs) are hypergraph decomposition methods successfully used for answering conjunctive queries and for solving constraint satisfaction problems. Every hypergraph H has a width relative to each of these methods: its hypertree width hw(H) , its generalized hypertree width ghw(H) , and its fractional hypertree width fhw(H) , respectively. It is known that hw(H)≤ k can be checked in polynomial time for fixed k , while checking ghw(H)≤ k is NP-complete for k ≥ 3 . The complexity of checking fhw(H)≤ k for a fixed k has been open for over a decade. We settle this open problem by showing that checking fhw(H)≤ k is NP-complete, even for k=2 . The same construction allows us to prove also the NP-completeness of checking ghw(H)≤ k for k=2 . After that, we identify meaningful restrictions that make checking for bounded ghw or fhw tractable or allow for an efficient approximation of the fhw .

scholarly journals Fast and Parallel Decomposition of Constraint Satisfaction Problems

2020 ◽  
Author(s):  
Georg Gottlob ◽  
Cem Okulmus ◽  
Reinhard Pichler
Keyword(s):  
Structural Properties ◽  
Constraint Satisfaction ◽  
Decomposition Methods ◽  
Constraint Satisfaction Problems ◽  
Query Answering ◽  
Conjunctive Query ◽  
Minimal Width ◽  
Parallel Decomposition

Constraint Satisfaction Problems (CSP) are notoriously hard. Consequently, powerful decomposition methods have been developed to overcome this complexity. However, this poses the challenge of actually computing such a decomposition for a given CSP instance, and previous algorithms have shown their limitations in doing so. In this paper, we present a number of key algorithmic improvements and parallelisation techniques to compute so-called Generalized Hypertree Decompositions (GHDs) faster. We thus advance the ability to compute optimal (i.e., minimal-width) GHDs for a significantly wider range of CSP instances on modern machines. This lays the foundation for more systems and applications in evaluating CSPs and related problems (such as Conjunctive Query answering) based on their structural properties.

scholarly journals Bipartite Encoding: A New Binary Encoding for Solving Non-Binary CSPs

2020 ◽  
Author(s):  
Ruiwei Wang ◽  
Roland H.C. Yap
Keyword(s):  
Constraint Satisfaction ◽  
State Of The Art ◽  
Constraint Satisfaction Problems ◽  
Special Structure ◽  
Large Set ◽  
Hidden Variable ◽  
Binary Constraints ◽  
Arc Consistency ◽  
Binary Encoding

Constraint Satisfaction Problems (CSPs) are typically solved with Generalized Arc Consistency (GAC). A general CSP can also be encoded into a binary CSP and solved with Arc Consistency (AC). The well-known Hidden Variable Encoding (HVE) is still a state-of-the-art binary encoding for solving CSPs. We propose a new binary encoding, called Bipartite Encoding (BE) which uses the idea of partitioning constraints. A BE encoded CSP can achieve a higher level of consistency than GAC on the original CSP. We give an algorithm for creating compact bipartite encoding for non-binary CSPs. We present a AC propagator on the binary constraints from BE exploiting their special structure. Experiments on a large set of non-binary CSP benchmarks with table constraints using the Wdeg, Activity and Impact heuristics show that BE with our AC propagator can outperform existing state-of-the-art GAC algorithms (CT, STRbit) and binary encodings (HVE with HTAC).

scholarly journals Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

2013 ◽  
Vol 44 (2) ◽  
pp. 131-156 ◽  
Author(s):  
Laura Climent ◽  
Richard J. Wallace ◽  
Miguel A. Salido ◽  
Federico Barber
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Satisfaction Problems ◽  
Robust Solutions

scholarly journals A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems

2011 ◽  
Vol 21 (4) ◽  
pp. 733-744 ◽  
Author(s):  
Marlene Arangú ◽  
Miguel Salido
Keyword(s):  
Constraint Satisfaction ◽  
Constraint Programming ◽  
Real Life ◽  
Search Space ◽  
Constraint Satisfaction Problems ◽  
Fine Grained ◽  
Arc Consistency ◽  
Life Problems ◽  
Programming Techniques ◽  
Np Complete

A fine-grained arc-consistency algorithm for non-normalized constraint satisfaction problems Constraint programming is a powerful software technology for solving numerous real-life problems. Many of these problems can be modeled as Constraint Satisfaction Problems (CSPs) and solved using constraint programming techniques. However, solving a CSP is NP-complete so filtering techniques to reduce the search space are still necessary. Arc-consistency algorithms are widely used to prune the search space. The concept of arc-consistency is bidirectional, i.e., it must be ensured in both directions of the constraint (direct and inverse constraints). Two of the most well-known and frequently used arc-consistency algorithms for filtering CSPs are AC3 and AC4. These algorithms repeatedly carry out revisions and require support checks for identifying and deleting all unsupported values from the domains. Nevertheless, many revisions are ineffective, i.e., they cannot delete any value and consume a lot of checks and time. In this paper, we present AC4-OP, an optimized version of AC4 that manages the binary and non-normalized constraints in only one direction, storing the inverse founded supports for their later evaluation. Thus, it reduces the propagation phase avoiding unnecessary or ineffective checking. The use of AC4-OP reduces the number of constraint checks by 50% while pruning the same search space as AC4. The evaluation section shows the improvement of AC4-OP over AC4, AC6 and AC7 in random and non-normalized instances.

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