An introduction to the theory of lists
Proceedings of the NATO Advanced Study Institute on Logic of programming and calculi of discrete design
Programming pearls
The maximum-segment-sum problem
Formal development programs and proofs
Programming: the derivation of algorithms
Programming: the derivation of algorithms
Left-bottom and right-top segments
Science of Computer Programming
A calculus of functions for program derivation
Research topics in functional programming
Science of Computer Programming
Real-time deques, multihead Turing machines, and purely functional programming
FPCA '93 Proceedings of the conference on Functional programming languages and computer architecture
Algebra of programming
Dynamic programming: a different perspective
Proceedings of the IFIP TC 2 WG 2.1 international workshop on Algorithmic languages and calculi
Make it practical: a generic linear-time algorithm for solving maximum-weightsum problems
ICFP '00 Proceedings of the fifth ACM SIGPLAN international conference on Functional programming
Program optimization using indexed and recursive data structures
PEPM '02 Proceedings of the 2002 ACM SIGPLAN workshop on Partial evaluation and semantics-based program manipulation
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
WABI '02 Proceedings of the Second International Workshop on Algorithms in Bioinformatics
Algebraic methods for optimization problems
Algebraic and coalgebraic methods in the mathematics of program construction
The classification of greedy algorithms
Science of Computer Programming
An Optimal Algorithm for the Maximum-Density Segment Problem
SIAM Journal on Computing
Journal of Computer and System Sciences
An optimal algorithm for maximum-sum segment and its application in bioinformatics
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Generation of efficient programs for solving maximum multi-marking problems
SAIG'01 Proceedings of the 2nd international conference on Semantics, applications, and implementation of program generation
Disjoint segments with maximum density
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Synthesis of fast programs for maximum segment sum problems
GPCE '09 Proceedings of the eighth international conference on Generative programming and component engineering
Algebra of programming in agda: Dependent types for relational program derivation
Journal of Functional Programming
A Short Cut to Optimal Sequences
APLAS '09 Proceedings of the 7th Asian Symposium on Programming Languages and Systems
FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
Proceedings of the 2013 International Workshop on Programming Models and Applications for Multicores and Manycores
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It may be surprising that variations of the maximum segment sum (MSS) problem, a textbook example for the squiggolists, are still active topics for algorithm designers. In this paper we examine the new developments from the view of relational program calculation. It turns out that, while the classical MSS problem is solved by the Greedy Theorem, by applying the Thinning Theorem, we get a linear-time algorithm for MSS with upper bound on length. To derive a linear-time algorithm for the em maximum segment density problem, on the other hand, we purpose a variation of thinning based on an extended notion of monotonicity. The concepts of left-negative and right-screw segments emerge from the search for monotonicity conditions. The efficiency of the resulting algorithms crucially relies on exploiting properties of the set of partial solutions and design efficient data structures for them.