Combinatorial interpretation of Kolmogorov complexity
Theoretical Computer Science
On characterization of entropy function via information inequalities
IEEE Transactions on Information Theory
Tractable hypergraph properties for constraint satisfaction and conjunctive queries
Proceedings of the forty-second ACM symposium on Theory of computing
Kolmogorov complexity as a language
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Worst-case optimal join algorithms: [extended abstract]
PODS '12 Proceedings of the 31st symposium on Principles of Database Systems
Tractable Hypergraph Properties for Constraint Satisfaction and Conjunctive Queries
Journal of the ACM (JACM)
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Our main result implies the following easily formulated statement. The set of edges E of every finite bipartite graph can be split into poly(log |E|) subsets so that all the resulting bipartite graphs are almost regular. The latter means that the ratio between the maximal and minimal non-zero degree of the left nodes is bounded by a constant and the same condition holds for the right nodes. Stated differently, every finite 2-dimensional set S ⊂ N2 can be partitioned into poly(log |S|) parts so that in every part the ratio between the maximal size and the minimal size of non-empty horizontal section is bounded by a constant and the same condition holds for vertical sections. We prove a similar statement for n-dimensional sets for any n and show how it can be used to relate information inequalities for Shannon entropy of random variables to inequalities between sizes of sections and their projections of multi-dimensional finite sets.