Maximum weight clique algorithms for circular-arc graphs and circle graphs
SIAM Journal on Computing
Representation and classification of coxeter monoids
European Journal of Combinatorics
New clique and independent set algorithms for circle graphs
Discrete Applied Mathematics
Text algorithms
Approximately matching context-free languages
Information Processing Letters
Let sleeping files lie: pattern matching in Z-compressed files
Journal of Computer and System Sciences
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
A fast algorithm for computing longest common subsequences
Communications of the ACM
On line arrangements in the hyperbolic plane
European Journal of Combinatorics
Algorithms on Compressed Strings and Arrays
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
On the longest increasing subsequence of a circular list
Information Processing Letters
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Semi-local longest common subsequences in subquadratic time
Journal of Discrete Algorithms
Window subsequence problems for compressed texts
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
All semi-local longest common subsequences in subquadratic time
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Querying and embedding compressed texts
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
Processing compressed texts: a tractability border
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
New algorithms for efficient parallel string comparison
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
Cycle detection and correction
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Multiplication algorithms for Monge matrices
SPIRE'10 Proceedings of the 17th international conference on String processing and information retrieval
Towards approximate matching in compressed strings: local subsequence recognition
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
Note: A fast algorithm for multiplying min-sum permutations
Discrete Applied Mathematics
Monge properties of sequence alignment
Theoretical Computer Science
A new algorithm for the characteristic string problem under loose similarity criteria
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Cycle detection and correction
ACM Transactions on Algorithms (TALG)
Faster algorithm for computing the edit distance between SLP-Compressed strings
SPIRE'12 Proceedings of the 19th international conference on String Processing and Information Retrieval
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Monge matrices play a fundamental role in optimisation theory, graph and string algorithms. Distance multiplication of two Monge matrices of size n can be performed in time O(n2). Motivated by applications to string algorithms, we introduced in previous works a subclass of Monge matrices, that we call simple unit-Monge matrices. We also gave a distance multiplication algorithm for such matrices, running in time O(n1.5). Landau asked whether this problem can be solved in linear time. In the current work, we give an algorithm running in time O(n log n), thus approaching an answer to Landau's question within a logarithmic factor. The new algorithm implies immediate improvements in running time for a number of algorithms on strings and graphs. In particular, we obtain an algorithm for finding a maximum clique in a circle graph in time O(n log2 n), and a surprisingly efficient algorithm for comparing compressed strings. We also point to potential applications in group theory, by making a connection between unit-Monge matrices and Coxeter monoids. We conclude that unit-Monge matrices are a fascinating object and a powerful tool, that deserves further study from both the mathematical and the algorithmic viewpoints.