Abstract. Consider a puzzle consisting of n tokens on an n-vertex graph, where each token has a distinct starting vertex and a distinct target vertex it wants to reach, and the only allowed transformation is to swap the tokens on adjacent vertices. We prove that every such puzzle is solvable in O(n 2 ) token swaps, and thus focus on the problem of minimizing the number of token swaps to reach the target token placement. We give a polynomial-time 2-approximation algorithm for trees, and using this, obtain a polynomial-time 2α-approximation algorithm for graphs whose tree α-spanners can be computed in polynomial time. Finally, we show that the problem can be solved exactly in polynomial time on complete bipartite graphs.
Abstract. Consider a puzzle consisting of n tokens on an n-vertex graph, where each token has a distinct starting vertex and a distinct target vertex it wants to reach, and the only allowed transformation is to swap the tokens on adjacent vertices. We prove that every such puzzle is solvable in O(n 2 ) token swaps, and thus focus on the problem of minimizing the number of token swaps to reach the target token placement. We give a polynomial-time 2-approximation algorithm for trees, and using this, obtain a polynomial-time 2α-approximation algorithm for graphs whose tree α-spanners can be computed in polynomial time. Finally, we show that the problem can be solved exactly in polynomial time on complete bipartite graphs.
For a transaction database, a frequent itemset is an itemset included in at least a specified number of transactions. To find all the frequent itemsets, the heaviest task is the computation of frequency of each candidate itemset. In the previous studies, there are roughly three data structures and algorithms for the computation: bitmap, prefix tree, and array lists. Each of these has its own advantage and disadvantage with respect to the density of the input database. In this paper, we propose an efficient way to combine these three data structures so that in any case the combination gives the best performance.
ABSTRACTFor a transaction database, a frequent itemset is an itemset included in at least a specified number of transactions. To find all the frequent itemsets, the heaviest task is the computation of frequency of each candidate itemset. In the previous studies, there are roughly three data structures and algorithms for the computation: bitmap, prefix tree, and array lists. Each of these has its own advantage and disadvantage with respect to the density of the input database. In this paper, we propose an efficient way to combine these three data structures so that in any case the combination gives the best performance.
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