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TopK Nearest Keyword Search on Large Graphs
"... It is quite common for networks emerging nowadays to have labels or textual contents on the nodes. On such networks, we study the problem of topk nearest keyword (kNK) search. In a network G modeled as an undirected graph, each node is attached with zero or more keywords, and each edge is assigned ..."
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It is quite common for networks emerging nowadays to have labels or textual contents on the nodes. On such networks, we study the problem of topk nearest keyword (kNK) search. In a network G modeled as an undirected graph, each node is attached with zero or more keywords, and each edge is assigned with a weight measuring its length. Given a query node q in G and a keyword λ, a kNK query seeks k nodes which contain λ and are nearest to q. kNK is not only useful as a standalone query but also as a building block for tackling complex graph pattern matching problems. The key to an accurate kNK result is a precise shortest distance estimation in a graph. Based on the latest distance oracle technique, we build a shortest path tree for a distance oracle and use the tree distance as a more accurate estimation. With such representation, the original kNK query on a graph can be reduced to answering the query on a set of trees and then assembling the results obtained from the trees. We propose two efficient algorithms to report the exact kNK result on a tree. One is query time optimized for a scenario when a small number of result nodes are of interest to users. The other handles kNK queries for an arbitrarily large k efficiently. In obtaining a kNK result on a graph from that on trees, a global storage technique is proposed to further reduce the index size and the query time. Extensive experimental results conform with our theoretical findings, and demonstrate the effectiveness and efficiency of our kNK algorithms on large real graphs. 1.
3sum hardness in (dynamic) data structures
 CoRR
"... We prove lower bounds for several (dynamic) data structure problems conditioned on the well known conjecture that 3SUM cannot be solved in O(n2−Ω(1)) time. This continues a line of work that was initiated by Pǎtraşcu [STOC 2010] and strengthened recently by Abboud and VassilevskaWilliams [FOCS 20 ..."
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We prove lower bounds for several (dynamic) data structure problems conditioned on the well known conjecture that 3SUM cannot be solved in O(n2−Ω(1)) time. This continues a line of work that was initiated by Pǎtraşcu [STOC 2010] and strengthened recently by Abboud and VassilevskaWilliams [FOCS 2014]. The problems we consider are from several subfields of algorithms, including text indexing, dynamic and fault tolerant graph problems, and distance oracles. In particular we prove polynomial lower bounds for the data structure version of the following problems: Dictionary Matching with Gaps, Document Retrieval problems with more than one pattern or an excluded pattern, Maximum Cardinality Matching in bipartite graphs (improving known lower bounds), dfailure Connectivity Oracles, Preprocessing for Induced Subgraphs, and Distance Oracles for Colors. Our lower bounds are based on several reductions from 3SUM to a special set intersection problem introduced by Pǎtraşcu, which we call Pǎtraşcu’s Problem. In particular, we provide a new reduction from 3SUM to Pǎtraşcu’s Problem which allows us to obtain stronger conditional lower bounds for (some) problems that have already been shown to be 3SUM hard, and for several of the problems examined here. Our other lower bounds are based on reductions from the Convolution3SUM problem, which was introduced by Pǎtraşcu. We also prove that up to a logarithmic factor, the Convolution3SUM problem is equivalent to 3SUM when the inputs are integers. A previous reduction of Pǎtraşcu shows that a subquadratic algorithm for Convolution3SUM implies a similarly subquadratic 3SUM algorithm, but not that the two problems are asymptotically equivalent or nearly equivalent. 1
Improved distance oracles and spanners for vertexlabeled graphs
 of Lecture Notes in Computer Science
, 2012
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Efficiently Computing TopK Shortest Path Join
"... Driven by many applications, in this paper we study the problem of computing the topk shortest paths from one set of target nodes to another set of target nodes in a graph, namely the topk shortest path join (KPJ) between two sets of target nodes. While KPJ is an extension of the problem of comput ..."
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Driven by many applications, in this paper we study the problem of computing the topk shortest paths from one set of target nodes to another set of target nodes in a graph, namely the topk shortest path join (KPJ) between two sets of target nodes. While KPJ is an extension of the problem of computing the topk shortest paths (KSP) between two target nodes, the existing technique by converting KPJ to KSP has several deficiencies in conducting the computation. To resolve these, we propose to use the bestfirst paradigm to recursively divide search subspaces into smaller subspaces, and to compute the shortest path in each of the subspaces in a prioritized order based on their lower bounds. Consequently, we only compute shortest paths in subspaces whose lower bounds are larger than the length of the current kth shortest path. To improve the efficiency, we further propose an iteratively bounding approach to tightening lower bounds of subspaces. Moreover, we propose two index structures which can be used to reduce the exploration area of a graph dramatically; these greatly speed up the computation. Extensive performance studies based on real road networks demonstrate the scalability of our approaches and that our approaches outperform the existing approach by several orders of magnitude. Furthermore, our approaches can be immediately used to compute KSP. Our experiment also demonstrates that our techniques outperform the stateoftheart algorithm for KSP by several orders of magnitude. 1.
Dynamic Steiner Tree and Subgraph TSP
"... In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an nvertex graph G = (V,E,w) with positive real edge weights, and our goal is to maintain a tree inG which is a good approximation of the minimum Steiner tree spanning a termina ..."
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In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an nvertex graph G = (V,E,w) with positive real edge weights, and our goal is to maintain a tree inG which is a good approximation of the minimum Steiner tree spanning a terminal set S ⊆ V, which changes over time. The changes applied to the terminal set are either terminal additions (incremental scenario), terminal removals (decremental scenario), or both (fully dynamic scenario). Our task here is twofold. We want to support updates in sublinear o(n) time, and keep the approximation factor of the algorithm as small as possible. The Steiner tree problem is one of the core problems in combinatorial optimization. It has been studied in many different settings, starting from classical approximation algorithms, through online and stochastic models, ending with game theoretic approaches. However, almost no progress has been made in the dynamic setting. The reason for this seems to be the lack of tools in both online approximation algorithms and dynamic algorithms. In this paper we develop appropriate methods that contribute to both these areas. The first ingredient belongs to the area of online algorithms. We prove that it is possible to