A Circuit-Based Approach to Efficient Enumeration

We study the problem of enumerating the satisfying valuations of a circuit while bounding the delay, i.e., the time needed to compute each successive valuation. We focus on the class of structured d-DNNF circuits originally introduced in knowledge compilation, a sub-area of artificial intelligence. We propose an algorithm for these circuits that enumerates valuations with linear preprocessing and delay linear in the Hamming weight of each valuation. Moreover, valuations of constant Hamming weight can be enumerated with linear preprocessing and constant delay. Our results yield a framework for efficient enumeration that applies to all problems whose solutions can be compiled to structured d-DNNFs. In particular, we use it to recapture classical results in database theory, for factorized database representations and for MSO evaluation. This gives an independent proof of constant-delay enumeration for MSO formulae with first-order free variables on bounded-treewidth structures

Answering Conjunctive Queries under Updates

We consider the task of enumerating and counting answers to $k$-ary conjunctive queries against relational databases that may be updated by inserting or deleting tuples. We exhibit a new notion of q-hierarchical conjunctive queries and show that these can be maintained efficiently in the following sense. During a linear time preprocessing phase, we can build a data structure that enables constant delay enumeration of the query results; and when the database is updated, we can update the data structure and restart the enumeration phase within constant time. For the special case of self-join free conjunctive queries we obtain a dichotomy: if a query is not q-hierarchical, then query enumeration with sublinear$^\ast$ delay and sublinear update time (and arbitrary preprocessing time) is impossible. For answering Boolean conjunctive queries and for the more general problem of counting the number of solutions of k-ary queries we obtain complete dichotomies: if the query's homomorphic core is q-hierarchical, then size of the the query result can be computed in linear time and maintained with constant update time. Otherwise, the size of the query result cannot be maintained with sublinear update time. All our lower bounds rely on the OMv-conjecture, a conjecture on the hardness of online matrix-vector multiplication that has recently emerged in the field of fine-grained complexity to characterise the hardness of dynamic problems. The lower bound for the counting problem additionally relies on the orthogonal vectors conjecture, which in turn is implied by the strong exponential time hypothesis. $^\ast)$ By sublinear we mean $O(n^{1-\varepsilon})$ for some $\varepsilon>0$, where $n$ is the size of the active domain of the current database

On the Complexity of Enumerating the Answers to Well-designed Pattern Trees

Well-designed pattern trees (wdPTs) have been introduced as an extension of conjunctive queries to allow for partial matching - analogously to the OPTIONAL operator of the semantic web query language SPARQL. Several computational problems of wdPTs have been studied in recent years, such as the evaluation problem in various settings, the counting problem, as well as static analysis tasks including the containment and equivalence problems. Also restrictions needed to achieve tractability of these tasks have been proposed. In contrast, the problem of enumerating the answers to a wdPT has been largely ignored so far. In this work, we embark on a systematic study of the complexity of the enumeration problem of wdPTs. As our main result, we identify several tractable and intractable cases of this problem both from a classical complexity point of view and from a parameterized complexity point of view

Enumeration on Trees under Relabelings

We study how to evaluate MSO queries with free variables on trees, within the framework of enumeration algorithms. Previous work has shown how to enumerate answers with linear-time preprocessing and delay linear in the size of each output, i.e., constant-delay for free first-order variables. We extend this result to support relabelings, a restricted kind of update operations on trees which allows us to change the node labels. Our main result shows that we can enumerate the answers of MSO queries on trees with linear-time preprocessing and delay linear in each answer, while supporting node relabelings in logarithmic time. To prove this, we reuse the circuit-based enumeration structure from our earlier work, and develop techniques to maintain its index under node relabelings. We also show how enumeration under relabelings can be applied to evaluate practical query languages, such as aggregate, group-by, and parameterized queries

Constant-Delay Enumeration for Nondeterministic Document Spanners

We consider the information extraction framework known as document spanners, and study the problem of efficiently computing the results of the extraction from an input document, where the extraction task is described as a sequential variable-set automaton (VA). We pose this problem in the setting of enumeration algorithms, where we can first run a preprocessing phase and must then produce the results with a small delay between any two consecutive results. Our goal is to have an algorithm which is tractable in combined complexity, i.e., in the sizes of the input document and the VA; while ensuring the best possible data complexity bounds in the input document size, i.e., constant delay in the document size. Several recent works at PODS'18 proposed such algorithms but with linear delay in the document size or with an exponential dependency in size of the (generally nondeterministic) input VA. In particular, Florenzano et al. suggest that our desired runtime guarantees cannot be met for general sequential VAs. We refute this and show that, given a nondeterministic sequential VA and an input document, we can enumerate the mappings of the VA on the document with the following bounds: the preprocessing is linear in the document size and polynomial in the size of the VA, and the delay is independent of the document and polynomial in the size of the VA. The resulting algorithm thus achieves tractability in combined complexity and the best possible data complexity bounds. Moreover, it is rather easy to describe, in particular for the restricted case of so-called extended VAs. Finally, we evaluate our algorithm empirically using a prototype implementation.Comment: 29 pages. Extended version of arXiv:1807.09320. Integrates all corrections following reviewer feedback. Outside of some minor formatting differences and tweaks, this paper is the same as the paper to appear in the ACM TODS journa

Reaching for the light: The prioritization of conspicuous visual stimuli for reflexive target-directed reaching

The degree to which something stands out against the background of its environment communicates important information. The phenomenon of camouflage is a testament of the degree to which visual salience and probability of survival tend to overlap. Salient stimuli often elicit fast, reflexive movements in order to catch prey or avoid a predator. The overarching goal of the work presented in this thesis is to investigate how the physical salience of visual stimuli influence the programming and execution of reaching movements. I approached this question by recording kinematics and muscle responses during reaching movements. Broadly, this thesis investigates the effect of the physical salience of targets on the magnitude and latency of involuntary, spatially tuned muscle responses toward those targets. In Chapters 2 and 3, subjects reached toward an array of potential targets on a touchscreen. The final target was cued only after the reaching movement was initiated. From trial to trial, targets differed in their numerosity (i.e., how many on the left versus the right) and in their salience (i.e., their relative contrast with the background). Different amounts of delay were introduced between the appearance of the targets and the cue to move. The results from these two studies demonstrate that the physical salience of (i.e., the luminance contrast differences between) targets influences the timing and the magnitude of involuntary deviations toward the most salient target(s) during reaching movements. At the level of individual subjects, the degree to which someone involuntarily reached toward the salient stimulus was predicted by the relationship between processing speeds for the different target contrasts. In Chapter 4, subjects reached toward individual targets that varied in luminance contrast. Muscle activity in the right pectoralis major was recorded with intramuscular electrodes. Consistent with past studies, there was a consistent muscle response that was time-locked to the appearance of the target, regardless of the reaction time for the ensuing reaching movement. The same processing speed differences and magnitude modulations observed in Chapters 2 and 3 (due to different luminance contrast values of the targets) were observed in these stimulus-locked muscle responses. Further testing revealed that stimulus-locked responses were elicited by a delayed, spatially uninformative go-cue

Lest We Forget: Ladies\u27 Memorial Associations in Georgia and the Creation of the Lost Cause

Ladies\u27 Memorial Associations (LMAs) initially formed after the Civil War in order to provide proper burials for dead Confederate soldiers. Women in LMAs raised funds to beautify cemeteries and erect monuments. However, their work was hardly limited to caring for the dead as the actions of the LMAs can be considered the beginnings of the Lost Cause. Even if the LMAs did not necessarily realize it or intend it, their work was visibly political and had far-reaching implications, especially for a subsequent women\u27s group, the United Daughters of the Confederacy (UDC). Until now, little research has been conducted on the LMA chapters in Georgia. This work brings Southern women of the post-Civil War era back into the historical narrative and demonstrates their involvement in the creation of the Lost Cause