Carles Mateu

Edge Matching Puzzles as Hard SAT/CSP Benchmarks

Recently, edge matching puzzles, an NP-complete problem, have received, thanks to money-prized contests, considerable attention from wide audiences. This paper studies edge matching puzzles focusing on providing generation models of problem instances of variable hardness and on its resolution through the application of SAT and CSP techniques. From the generation side, we also identify the phase transition phenomena for each model. As solving methods, we employ both; SAT solvers through the translation to a SAT formula, and two ad-hoc CSP solvers we have developed, with different levels of consistency, employing generic and specialized heuristics. Finally, we conducted an extensive experimental investigation to identify the hardest generation models and the best performing solving techniques.

Optimizing Energy Consumption in Automated Vacuum Waste Collection Systems

Automated vacuum waste collection (AVWC) uses air suction on a closed network of underground pipes to transport waste from the drop off points scattered throughout the city to a central collection point, reducing greenhouse gas emissions and the inconveniences of conventional methods (odors, noise). Since a significant part of the cost of operating AVWC systems is energy consumption, we have started a project, together with a company that builds and installs such systems, with the aim of applying constraint programming technology to schedule the daily emptying sequences of the drop off points in such a way that energy consumption is minimized. In this paper we describe how the problem of deciding the drop off points that should be emptied at a given time can be modeled as a constraint integer programming (CIP) problem. Moreover, we report on experiments using real data from AVWC systems installed in different cities that provide empirical evidence that CIP offers a suitable technology for reducing energy consumption in AVWC.

Weighted argumentation for analysis of discussions in Twitter

Twitter has become a widely used social network to discuss ideas about many domains. This leads to a growing interest in understanding what are the major accepted or rejected opinions in different domains by social network users. At the same time, checking what are the topics that produce the most controversial discussions among users can be a good tool to discover topics that can be divisive, what can be useful, e.g., for policy makers. With the aim to automatically discover such information from Twitter discussions, we present an analysis system based on Valued Abstract Argumentation to model and reason about the accepted and rejected opinions. We consider different schemes to weight the opinions of Twitter users, such that we can tune the relevance of opinions considering different information sources from the social network. Towards having a fully automatic system, we also design a relation labeling system for discovering the relation between opinions. Regarding the underlying acceptability semantics, we use ideal semantics to compute accepted/rejected opinions. We define two measures over sets of accepted and rejected opinions to quantify the most controversial discussions. In order to validate our system, we analyze different real Twitter discussions from the political domain. The results show that different weighting schemes produce different sets of socially accepted opinions and that the controversy measures can reveal significant differences between discussions.

A predictor model for the composting process on an industrial scale based on Markov processes

The biochemical and physical characteristics of composting processes have been historically modeled from an analytic point of view. Recently, stochastic approaches pushed forward the short-term forecast for the observed behaviour, but no model deals well with long-term predictions, especially when dealing with industrial data. We present a new approach, based on Markov processes, that shows good accuracy when predicting the long-term evolution of composting processes on an industrial scale. The proposed model deals with incomplete industrial data even for unevenly spaced observations, learns from past observations improving accuracy as data grows, and shows excellent predictive capabilities for time spans larger than 200 days and for heterogeneous large scale compost windrows. With our model, predictions can be obtained in real-time using Monte-Carlo runs. The model may be extremely convenient for industrial environments where large amounts of incomplete available data make it very difficult to use other prediction approaches. We model the biochemical and physical characteristics of the composting process.This model can be used to predict the resulting compost.The model has been created with incomplete data, will be better with more data.This model is suitable for industrial scale processes.

How Hard is a Commercial Puzzle: the Eternity II Challenge

Recently, edge matching puzzles, an NP-complete problem, have received, thanks to money-prized contests, considerable attention from wide audiences. We consider these competitions not only a challenge for SAT/CSP solving techniques but also as an opportunity to showcase the advances in the SAT/CSP community to a general audience. This paper studies the NP-complete problem of edge matching puzzles focusing on providing generation models of problem instances of variable hardness and on its resolution through the application of SAT and CSP techniques. From the generation side, we also identify the phase transition phenomena for each model. As solving methods, we employ both; SAT solvers through the translation to a SAT formula, and two ad-hoc CSP solvers we have developed, with different levels of consistency, employing several generic and specialized heuristics. Finally, we conducted an extensive experimental investigation to identify the hardest generation models and the best performing solving techniques.

On the hardness of solving edge matching puzzles as SAT or CSP problems

Edge matching puzzles have been amongst us for a long time now and traditionally they have been considered, both, a children’s game and an interesting mathematical divertimento. Their main characteristics have already been studied, and their worst-case complexity has been properly classified as a NP-complete problem. It is in recent times, specially after being used as the problem behind a money-prized contest, with a prize of 2US

The Sudoku completion problem with rectangular hole pattern is NP-complete

million for the first solver, that edge matching puzzles have attracted mainstream attention from wider audiences, including, of course, computer science people working on solving hard problems. We consider these competitions as an interesting opportunity to showcase SAT/CSP solving techniques when confronted to a real world problem to a broad audience, a part of the intrinsic, i.e. monetary, interest of such a contest. This article studies the NP-complete problem known as edge matching puzzle using SAT and CSP approaches for solving it. We will focus on providing, first and foremost, a theoretical framework, including a generalized definition of the problem. We will design and show algorithms for easy and fast problem instances generation, generators with easily tunable hardness. Afterwards we will provide with SAT and CSP models for the problems and we will study problem complexity, both typical case and worst-case complexity. We will also provide some specially crafted heuristics that result in a boost in solving time and study which is the effect of such heuristics.

From High Girth Graphs to Hard Instances

Abstract The sudoku completion problem is a special case of the latin square completion problem and both problems are known to be NP-complete. However, in the case of a rectangular hole pattern–i.e. each column (or row) is either full or empty of symbols–it is known that the latin square completion problem can be solved in polynomial time. Conversely, we prove in this paper that the same rectangular hole pattern still leaves the sudoku completion problem NP-complete.

An argumentative approach for discovering relevant opinions in Twitter with probabilistic valued relationships

In this paper we provide a new method to generate hard k-SAT instances. Basically, we construct the bipartite incidence graph of a k-SAT instance where the left side represents the clauses and the right side represents the literals of our Boolean formula. Then, the clauses are filled by incrementally connecting both sides while keeping the girth of the graph as high as possible. That assures that the expansion of the graph is also high. It has been shown that high expansion implies high resolution width w. The resolution width characterizes the hardness of an instance Fof nvariables since if every resolution refutation of Fhas width wthen every resolution refutation requires size

Statistical modelling of CSP solving algorithms performance

2^{\Omega(w^2/n)}