Data structures and algorithms 3: multi-dimensional searching and computational geometry
Data structures and algorithms 3: multi-dimensional searching and computational geometry
Efficient data structures for range searching on a grid
Journal of Algorithms
Performance guarantees on a sweep-line heuristic for covering rectilinear polygons with rectangles
SIAM Journal on Discrete Mathematics
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
On the all-pairs-shortest-path problem in unweighted undirected graphs
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Fast Boolean Matrix Multiplication for Highly Clustered Data
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
Exact and Approximate Distances in Graphs - A Survey
ESA '01 Proceedings of the 9th Annual European Symposium on Algorithms
On Diameter Verification and Boolean Matrix Multiplication.
On Diameter Verification and Boolean Matrix Multiplication.
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
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For a Boolean matrix D, let rD be the minimum number of rectangles sufficient to cover exactly the rectilinear region formed by the 1-entries in D. Next, let mD be the minimum of the number of 0-entries and the number of 1-entries in D.Suppose that the rectilinear regions formed by the 1-entries in two n 脳 n Boolean matrices A and B totally with q edges are given. We show that in time 脮 (q + min{rArB, n(n + rA), n(n + rB)}) one can construct a data structure which for any entry of the Boolean product of A and B reports whether or not it is equal to 1, and if so, reports also the so called witness of the entry, in time O(log q).As a corollary, we infer that if the matrices A and B are given as input, their product and the witnesses of the product can be computed in time 脮 (n(n + min{rA, rB})). This implies in particular that the product of A and B and its witnesses can be computed in time Õ(n(n + min{mA, mB})).In contrast to the known sub-cubic algorithms for Boolean matrix multiplication based on arithmetic 0 - 1-matrix multiplication, our algorithms do not involve large hidden constants in their running time and are easy to implement.