The complexity of approximating conservative counting CSPs

We study the complexity of approximately solving the weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, there is a classification known for the case in which the domain of functions in F is Boolean. In this paper, we give a classification for the more general problem where functions in F have an arbitrary finite domain. We define the notions of weak log-modularity and weak log-supermodularity. We show that if F is weakly log-modular, then #CSP(F)is in FP. Otherwise, it is at least as difficult to approximate as #BIS, the problem of counting independent sets in bipartite graphs. #BIS is complete with respect to approximation-preserving reductions for a logically-defined complexity class #RHPi1, and is believed to be intractable. We further sub-divide the #BIS-hard case. If F is weakly log-supermodular, then we show that #CSP(F) is as easy as a (Boolean) log-supermodular weighted #CSP. Otherwise, we show that it is NP-hard to approximate. Finally, we give a full trichotomy for the arity-2 case, where #CSP(F) is in FP, or is #BIS-equivalent, or is equivalent in difficulty to #SAT, the problem of approximately counting the satisfying assignments of a Boolean formula in conjunctive normal form. We also discuss the algorithmic aspects of our classification.Comment: Minor revisio

An Overview of Models for Response Times and Processes in Cognitive Tests.

Response times (RTs) are a natural kind of data to investigate cognitive processes underlying cognitive test performance. We give an overview of modeling approaches and of findings obtained with these approaches. Four types of models are discussed: response time models (RT as the sole dependent variable), joint models (RT together with other variables as dependent variable), local dependency models (with remaining dependencies between RT and accuracy), and response time as covariate models (RT as independent variable). The evidence from these approaches is often not very informative about the specific kind of processes (other than problem solving, information accumulation, and rapid guessing), but the findings do suggest dual processing: automated processing (e.g., knowledge retrieval) vs. controlled processing (e.g., sequential reasoning steps), and alternative explanations for the same results exist. While it seems well-possible to differentiate rapid guessing from normal problem solving (which can be based on automated or controlled processing), further decompositions of response times are rarely made, although possible based on some of model approaches

A Trichotomy for Regular Simple Path Queries on Graphs

Regular path queries (RPQs) select nodes connected by some path in a graph. The edge labels of such a path have to form a word that matches a given regular expression. We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same nodes. Those regular simple path queries (RSPQs) find several applications in practice, yet they quickly become intractable, even for basic languages such as (aa)* or a*ba*. In this paper, we establish a comprehensive classification of regular languages with respect to the complexity of the corresponding regular simple path query problem. More precisely, we identify the fragment that is maximal in the following sense: regular simple path queries can be evaluated in polynomial time for every regular language L that belongs to this fragment and evaluation is NP-complete for languages outside this fragment. We thus fully characterize the frontier between tractability and intractability for RSPQs, and we refine our results to show the following trichotomy: Evaluations of RSPQs is either AC0, NL-complete or NP-complete in data complexity, depending on the regular language L. The fragment identified also admits a simple characterization in terms of regular expressions. Finally, we also discuss the complexity of the following decision problem: decide, given a language L, whether finding a regular simple path for L is tractable. We consider several alternative representations of L: DFAs, NFAs or regular expressions, and prove that this problem is NL-complete for the first representation and PSPACE-complete for the other two. As a conclusion we extend our results from edge-labeled graphs to vertex-labeled graphs and vertex-edge labeled graphs.Comment: 15 pages, conference submissio

Mixed labeling: Integration of internal and external labeling

Tato diplomová práce se zabývá automatickým rozmístěním popisků. Popisky mohou být umístěny přes daný objekt (angl. Internal Labelig) či vedle daného objektu (angl. External Labeling), přičemž jsou s ním spojeny čárou. V této práci se pokouším zkombinovat tyto dva přístupy a popisky umísťovat smíšeně. Zároveň se snažím popisky umístěné vně objektu umístit tak, aby k jejich asociaci s ním nebyla čára potřebná. V textu práce nejprve uvádím existující přístupy k této problematice. Následně analyzuji problémy spojené se smíšeným umísťováním popisků a na základně analýzy provádím implementaci. Funkčnost algoritmu je otestována na šesti modelech. Se třemi z nich je provedena uživatelská studie.This master thesis focuses on automatic label placement. Labels can be positioned over a given object (Internal Labeling) or next to it and connected by a line (External Labeling). I attempt to combine the two methods and position the labels in a mixed fashion. When I place the label next to the object, I try to pick such a position, that the line to connect it is not necessary. First, I present existing methods in the text. Subsequently, I analyze the problems related to mixed label placement. I carry out the implementation based on the analysis and test it with six models of various complexity. I evaluate with users in the end