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Deciding Monotone Duality and Identifying Frequent Itemsets in Quadratic Logspace
Data Structures and Algorithms · Submitted 9 Dec 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By exploiting a recent problem-decomposition method by Boros and Makino (ICALP 2009), we show that duality testing for hypergraphs, and thus for monotone DNFs, is feasible in DSPACE[log^2 n], i.e., in quadratic logspace.
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The abstract, sentence by sentence
The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph H consists of precisely all minimal transversals of a simple hypergraph G. By exploiting a recent problem-decomposition method by Boros and Makino (ICALP 2009), we show that duality testing for hypergraphs, and thus for monotone DNFs, is feasible in DSPACE[log^2 n], i.e., in quadratic logspace. As the monotone duality problem is equivalent to a number of problems in the areas of databases, data mining, and knowledge discovery, the results presented here yield new complexity results for those problems, too. For example, it follows from our results that whenever for a Boolean-valued relation (whose attributes represent items), a number of maximal frequent itemsets and a number of minimal infrequent itemsets are known, then it can be decided in quadratic logspace whether there exist additional frequent or infrequent itemsets.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. | background 1.00 | 0.09 | 0.03 | asserted 0.98 |
| s1 | This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph H consists of precisely all minimal transversals of a simple hypergraph G. | background 0.99 | 0.12 | 0.04 | asserted 1.00 |
| s2 | By exploiting a recent problem-decomposition method by Boros and Makino (ICALP 2009), we show that duality testing for hypergraphs, and thus for monotone DNFs, is feasible in DSPACE[log^2 n], i.e., in quadratic logspace. | result 0.73 | 0.94 | 0.87 | asserted 1.00 |
| s3 | As the monotone duality problem is equivalent to a number of problems in the areas of databases, data mining, and knowledge discovery, the results presented here yield new complexity results for those problems, too. | interpretation 0.99 | 0.66 | 0.14 | asserted 0.93 |
| s4 | For example, it follows from our results that whenever for a Boolean-valued relation (whose attributes represent items), a number of maximal frequent itemsets and a number of minimal infrequent itemsets are known, then it can be decided in quadratic logspace whether there exist additional frequent or infrequent itemsets. | interpretation 0.67 | 0.85 | 0.10 | asserted 0.96 |
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Original abstract
The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph H consists of precisely all minimal transversals of a simple hypergraph G. By exploiting a recent problem-decomposition method by Boros and Makino (ICALP 2009), we show that duality testing for hypergraphs, and thus for monotone DNFs, is feasible in DSPACE[log^2 n], i.e., in quadratic logspace. As the monotone duality problem is equivalent to a number of problems in the areas of databases, data mining, and knowledge discovery, the results presented here yield new complexity results for those problems, too. For example, it follows from our results that whenever for a Boolean-valued relation (whose attributes represent items), a number of maximal frequent itemsets and a number of minimal infrequent itemsets are known, then it can be decided in quadratic logspace whether there exist additional frequent or infrequent itemsets.
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