Finding Top-k Min-Cost Connected Trees in Databases

Abstract

It is widely realized that the integration of database and information retrieval techniques will provide users with a wide range of high quality services. In this paper, we study processing an l-keyword query, p 1 , p 2 , · · · , p l , against a relational database which can be modeled as a weighted graph, G(V, E). Here V is a set of nodes (tuples) and E is a set of edges representing foreign key references between tuples. Let V i ⊆ V be a set of nodes that contain the keyword p i . We study finding top-k minimum cost connected trees that contain at least one node in every subset V i , and denote our problem as GST-k. When k = 1, it is known as a minimum cost group Steiner tree problem which is NPComplete. We observe that the number of keywords, l, is small, and propose a novel parameterized solution, with l as a parameter, to find the optimal GST-1, in time complexity O(3 l n + 2 l ((l + log n)n + m)), where n and m are the numbers of nodes and edges in graph G. Our solution can handle graphs with a large number of nodes. Our GST-1 solution can be easily extended to support GST-k, which outperforms the existing GST-k solutions over both weighted undirected/directed graphs. We conducted extensive experimental studies, and report our finding.

Parameterized Complexity of Arc-Weighted Directed Steiner Problems

“…In this case there must be an arc from some vertex in D to some vertex in ▯ So far, we neglected studying (0-)DST. It is already known from the literature that DST is FPT for both single parameterizations by l and p∕ min W [8], [12], while 0-DST is FPT with respect to l [8], [12] and it is W[2]-hard with respect to p∕ min W [11]. We can add to these results a proof for the presumable nonexistence of a polynomial-size problem kernel for DST parameterized by the combined parameter ðl; p∕ min W Þ.…”

Keyword Query Expansion Paradigm Based on Recommendation and Interpretation in Relational Databases

“…end if (19) end foreach; (20) if (IsAN == TRUE) then (21) .remove( ); (22) end if (23) end for (24) end if (25) if ( is not Null) then (26) for = 1 to | | do (27) scan Table AV …”

“…Although these methods store the abstract structural information and take little memory, the generation process of CNs needs to take a huge amount of time. Correspondingly, in [22][23][24][25][26][27] the database is modeled as a data graph, where nodes represent tuples and edges represent primary-foreign-key relationships between tuples. The methods identify the minimum connection trees that contain the keywords on the data graph.…”

Online Multi-keywords Map-search Algorithm Based on Sub-region Method

“…As for tuple-based keyword search, it should construct a spanning tree. BANKS-I [6]proposedthe Reverse Search Algorithmthat processesDijkstraalgorithm on the keywords tuples to find the Shortest Path's shared nodes in the tree as a tree's root.Then it searches the nodes containing keywords put on the root as search results.Since the number of executions of the Dijkstraalgorithm is proportional to the number of tuples that contain the keywords, the query results are in a lower efficiency.BANKS-II [7] provided a Bidirectional expansion algorithm thatimproves the BANKS-I algorithm,but it will cause lower quality problem because it loses some minimum spanning paths in computation stage.DPBF [8]chose a node containing keywords as the starting point , alternately performed its definition grow and merge functions, until all the nodes are packages that contain the keywordin the same group containing one tuple connection tree.…”