Queries revisited

AbstractWe begin with a brief tutorial on the problem of learning a finite concept class over a finite domain using membership queries and/or equivalence queries. We then sketch general results on the number of queries needed to learn a class of concepts, focusing on the various notions of combinatorial dimension that have been employed, including the teaching dimension, the exclusion dimension, the extended teaching dimension, the fingerprint dimension, the sample exclusion dimension, the Vapnik–Chervonenkis dimension, the abstract identification dimension, and the general dimension

The complexity of acyclic conjunctive queries revisited

In this paper, we consider first-order logic over unary functions and study the complexity of the evaluation problem for conjunctive queries described by such kind of formulas. A natural notion of query acyclicity for this language is introduced and we study the complexity of a large number of variants or generalizations of acyclic query problems in that context (Boolean or not Boolean, with or without inequalities, comparisons, etc...). Our main results show that all those problems are \textit{fixed-parameter linear} i.e. they can be evaluated in time $f(|Q|).|\textbf{db}|.|Q(\textbf{db})|$ where $|Q|$ is the size of the query $Q$, $|\textbf{db}|$ the database size, $|Q(\textbf{db})|$ is the size of the output and $f$ is some function whose value depends on the specific variant of the query problem (in some cases, $f$ is the identity function). Our results have two kinds of consequences. First, they can be easily translated in the relational (i.e., classical) setting. Previously known bounds for some query problems are improved and new tractable cases are then exhibited. Among others, as an immediate corollary, we improve a result of \~\cite{PapadimitriouY-99} by showing that any (relational) acyclic conjunctive query with inequalities can be evaluated in time $f(|Q|).|\textbf{db}|.|Q(\textbf{db})|$. A second consequence of our method is that it provides a very natural descriptive approach to the complexity of well-known algorithmic problems. A number of examples (such as acyclic subgraph problems, multidimensional matching, etc...) are considered for which new insights of their complexity are given.Comment: 30 page

Practical Range Minimum Queries Revisited

Finding the position of the minimal element in a subarray A[i..j] of an array A of size n is a fundamental operation in many applications. In 2011, Fischer and Heun presented the first index of size 2n+o(n) bits which answers the operation in constant time for any subarray. The index can be computed in linear time and queries can be answered without consulting the original array. The most recent and currently fastest practical index is due to Ferrada and Navarro (DCC\u2716). It reduces the range minimum query (RMQ) to more fundamental and well studied queries on binary vectors, namely rank and select, and a RMQ query on an array of sublinear size derived from A. A range min-max tree is employed to solve this recursive RMQ call. In this paper, we review their practical design and suggest a series of changes which result in consistently faster query times. Specifically, we provide a customized select implementation, switch to two levels of recursion, and use the sparse table solution for the recursion base case instead of a range min-max tree. We provide an extensive empirical evaluation of our new implementation and also compare it to the state of the art. Our experimental study shows that our proposal significantly outperforms the previous solutions on established benchmarks (up to a factor of three) and furthermore accelerates real world applications such as traversing a succinct tree or listing all distinct elements in an interval of an array

Path Planning on Roads using Cache

In Path Planning Cache(PPC) it forces to respond to the new problem with the help of somewhat coordinated queries. When the original doubt matches utterly only then a query that is cached is revisited. Sometimes there may be chances that the elements of cache might not be superior and not be able to take action to the asked queries for the craze that have arrived only just. To locate a direction involving an asked-for locality to the target by making use of the direction-finding practices via the mobile, where the on-road pathway scheduling is vital function

The Adaptive Sampling Revisited

The problem of estimating the number $n$ of distinct keys of a large collection of $N$ data is well known in computer science. A classical algorithm is the adaptive sampling (AS). $n$ can be estimated by $R.2^D$, where $R$ is the final bucket (cache) size and $D$ is the final depth at the end of the process. Several new interesting questions can be asked about AS (some of them were suggested by P.Flajolet and popularized by J.Lumbroso). The distribution of $W=\log (R2^D/n)$ is known, we rederive this distribution in a simpler way. We provide new results on the moments of $D$ and $W$. We also analyze the final cache size $R$ distribution. We consider colored keys: assume that among the $n$ distinct keys, $n_C$ do have color $C$. We show how to estimate $p=\frac{n_C}{n}$. We also study colored keys with some multiplicity given by some distribution function. We want to estimate mean an variance of this distribution. Finally, we consider the case where neither colors nor multiplicities are known. There we want to estimate the related parameters. An appendix is devoted to the case where the hashing function provides bits with probability different from $1/2$

Characterizations of User Web Revisit Behavior

In this article we update and extend on earlier long-term studies on user's page revisit behavior. Revisits ar

Encoding Two-Dimensional Range Top-k Queries Revisited

We consider the problem of encoding two-dimensional arrays, whose elements come from a total order, for answering Top-k queries. The aim is to obtain encodings that use space close to the information-theoretic lower bound, which can be constructed efficiently. For 2 x n arrays, we first give upper and lower bounds on space for answering sorted and unsorted 3-sided Top-k queries. For m x n arrays, with m <=n and k <=mn, we obtain (m lg{(k+1)n choose n}+4nm(m-1)+o(n))-bit encoding for answering sorted 4-sided Top-k queries. This improves the min{(O(mn lg{n}),m^2 lg{(k+1)n choose n} + m lg{m}+o(n))}-bit encoding of Jo et al. [CPM, 2016] when m = o(lg{n}). This is a consequence of a new encoding that encodes a 2 x n array to support sorted 4-sided Top-k queries on it using an additional 4n bits, in addition to the encodings to support the Top-k queries on individual rows. This new encoding is a non-trivial generalization of the encoding of Jo et al. [CPM, 2016] that supports sorted 4-sided Top-2 queries on it using an additional 3n bits. We also give almost optimal space encodings for 3-sided Top-k queries, and show lower bounds on encodings for 3-sided and 4-sided Top-k queries