Showing papers by "Kunihiko Sadakane published in 2020"

Efficient query autocompletion with edit distance-based error tolerance

Abstract: Query autocompletion is an important feature saving users many keystrokes from typing the entire query. In this paper, we study the problem of query autocompletion that tolerates errors in users’ input using edit distance constraints. Previous approaches index data strings in a trie, and continuously maintain all the prefixes of data strings whose edit distances from the query string are within the given threshold. The major inherent drawback of these approaches is that the number of such prefixes is huge for the first few characters of the query string and is exponential in the alphabet size. This results in slow query response even if the entire query approximately matches only few prefixes. We propose a novel neighborhood generation-based method to process error-tolerant query autocompletion. Our proposed method only maintains a small set of active nodes, thus saving both space and time to process the query. We also study efficient duplicate removal, a core problem in fetching query answers, and extend our method to support top-k queries. Optimization techniques are proposed to reduce the index size. The efficiency of our method is demonstrated through extensive experiments on real datasets.

Optimal In-place Algorithms for Basic Graph Problems

Abstract: We present linear time in-place algorithms for several fundamental graph problems including the well-known graph search methods (like depth-first search, breadth-first search, maximum cardinality search), connectivity problems (like biconnectivity, 2-edge connectivity), decomposition problem (like chain decomposition) among various others, improving the running time (by polynomial multiplicative factor) of the recent results of Chakraborty et al. [ESA, 2018] who designed \(O(n^3 \lg n)\) time in-place algorithms for some of the above mentioned problems. The running times of all our algorithms are essentially optimal as they run in linear time. One of the main ideas behind obtaining these algorithms is the detection and careful exploitation of sortedness present in the input representation for any graph without loss of generality. This observation alone is powerful enough to design some basic linear time in-place algorithms, but more non-trivial graph problems require extra techniques which, we believe, may find other applications while designing in-place algorithms for different graph problems in future.

Compressed Orthogonal Search on Suffix Arrays with Applications to Range LCP.

Abstract: We propose a space-efficient data structure for orthogonal range search on suffix arrays. For general two-dimensional orthogonal range search problem on a set of n points, there exists an n logn(1+o(1))bit data structure supporting O(logn)-time counting queries [Mäkinen, Navarro 2007]. The space matches the information-theoretic lower bound. However, if we focus on a point set representing a suffix array, there is a chance to obtain a space efficient data structure. We answer this question affirmatively. Namely, we propose a data structure for orthogonal range search on suffix arrays which uses O( 1 ε n(H0 + 1)) bits where H0 is the order-0 entropy of the string and answers a counting query in O(n) time for any constant ε > 0. As an application, we give an O( 1 ε n(H0 + 1))-bit data structure for the range LCP problem. 2012 ACM Subject Classification Theory of computation → Models of computation

Succinct Navigational Oracles for Families of Intersection Graphs on a Circle.

Abstract: We consider the problem of designing succinct navigational oracles, i.e., succinct data structures supporting basic navigational queries such as degree, adjacency, and neighborhood efficiently for intersection graphs on a circle, which include graph classes such as {\it circle graphs}, {\it $k$-polygon-circle graphs}, {\it circle-trapezoid graphs}, {\it trapezoid graphs}. The degree query reports the number of incident edges to a given vertex, the adjacency query asks if there is an edge between two given vertices, and the neighborhood query enumerates all the neighbors of a given vertex. We first prove a general lower bound for these intersection graph classes and then present a uniform approach that lets us obtain matching lower and upper bounds for representing each of these graph classes. More specifically, our lower bound proofs use a unified technique to produce tight bounds for all these classes, and this is followed by our data structures which are also obtained from a unified representation method to achieve succinctness for each class. In addition, we prove a lower bound of space for representing {\it trapezoid} graphs and give a succinct navigational oracle for this class of graphs.

Storing Set Families More Compactly with Top ZDDs

Abstract: Zero-suppressed Binary Decision Diagrams (ZDDs) are data structures for representing set families in a compressed form. With ZDDs, many valuable operations on set families can be done in time polynomial in ZDD size. In some cases, however, the size of ZDDs for representing large set families becomes too huge to store them in the main memory. This paper proposes top ZDD, a novel representation of ZDDs which uses less space than existing ones. The top ZDD is an extension of top tree, which compresses trees, to compress directed acyclic graphs by sharing identical subgraphs. We prove that navigational operations on ZDDs can be done in time poly-logarithmicin ZDD size, and show that there exist set families for which the size of the top ZDD is exponentially smaller than that of the ZDD. We also show experimentally that our top ZDDs have smaller size than ZDDs for real data.

Enumerating Range Modes

Abstract: Given a sequence of elements, we consider the problem of indexing the sequence to support range mode queries - given a query range, find the element with maximum frequency in the range. We give indexing data structures for this problem; given a sequence, we construct a data structure that can be used later to process arbitrary queries. Our algorithms are efficient for small maximum frequency cases. We also consider a natural generalization of the problem: the range mode enumeration problem, for which there has been no known efficient algorithms. Our algorithms have query time complexities which are linear in the output size plus small terms.

Compact and succinct data structures for multidimensional orthogonal range searching

Abstract: We introduce compact and succinct representations of a d-dimensional point set for any constant d ≥ 3 supporting orthogonal range searching. Our first data structure uses d n lg ⁡ n + o ( n lg ⁡ n ) bits, where n denotes the number of points in P, and supporting reporting queries in O ( ( n ( d − 2 ) / d + occ ) lg ⁡ n / lg ⁡ lg ⁡ n ) time, and counting queries in O ( n ( d − 2 ) / d lg ⁡ n / lg ⁡ lg ⁡ n ) time, where occ denotes the number of point to report, which is faster than known algorithms. Our second data structure uses d n lg ⁡ U − n lg ⁡ n + o ( n lg ⁡ n ) bits, where U is the size of the universe, which asymptotically matches the information-theoretic lower bound. The query time complexity is worse than the first one, but the algorithm runs fast in practical database search.