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Extra resources for Actes du Congrès international des mathématiciens: 1 10 Septembre 1970 NICE France

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We need to investigate this further by considering another changing point in Li . This is handled by moving q towards Q for continuing the binary search. Intuitively, this abandons the half part of Li that no point inside there could dominate/is dominated by Q. Finally, if we exit the while loop, it means no changing points in Li can dominate Q and vice versa, we know that Q dominates Li in this case due to Lemma 4. The correctness of the algorithm is provided by the following Lemma. Lemma 5. Algorithm 1 correctly determines the line-point dominance relationship between Li and Q.

The proposed algorithm, called ATQ, utilizes the following two strategies to prune the search space: 1. Target-oriented search. Since our query allows users to specify their search intention, we make use of the schema graph to direct the search to the relevant nodes. 2. Time-aware pruning. Given that our query contains temporal constraints, we augment nodes in the data graph with time boundaries to quickly determine if a subtree can satisfy the time constraints. Subtrees that cannot satisfy the time constraints will not be explored.

Algorithm reverseSearch (see Algorithm 2) takes as input a partial answer tree and tries to construct the complete answer by finding nodes that match the remaining keywords in Kbody . It also uses a stack NodeStack to keep track of the nodes to be processed and calls function getRelevantN eighbours() to find the set of nodes to traverse next (Lines 5–6). For each node u to be traversed, if u matches a keyword in Kbody , we check that u satisfies the time constraints and connect u to the answer tree (Lines 7–10).

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Actes du Congrès international des mathématiciens: 1 10 Septembre 1970 NICE France by Comité d'Organisation du Congrès

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