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A survey on combinatorial optimization in dynamic environments∗

Nicolas Boria, Vangelis T. Paschos (2011)

RAIRO - Operations Research

This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The...

A survey on combinatorial optimization in dynamic environments∗

Nicolas Boria, Vangelis T. Paschos (2011)

RAIRO - Operations Research

This survey presents major results and issues related to the study of NPO problems in dynamic environments, that is, in settings where instances are allowed to undergo some modifications over time. In particular, the survey focuses on two complementary frameworks. The first one is the reoptimization framework, where an instance I that is already solved undergoes some local perturbation. The goal is then to make use of the information provided by the initial solution to compute a new solution. The...

A weighted graph polynomial from chromatic invariants of knots

Steven D. Noble, Dominic J. A. Welsh (1999)

Annales de l'institut Fourier

Motivated by the work of Chmutov, Duzhin and Lando on Vassiliev invariants, we define a polynomial on weighted graphs which contains as specialisations the weighted chromatic invariants but also contains many other classical invariants including the Tutte and matching polynomials. It also gives the symmetric function generalisation of the chromatic polynomial introduced by Stanley. We study its complexity and prove hardness results for very restricted classes of graphs.

Abelian periods, partial words, and an extension of a theorem of Fine and Wilf

Francine Blanchet-Sadri, Sean Simmons, Amelia Tebbe, Amy Veprauskas (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Recently, Constantinescu and Ilie proved a variant of the well-known periodicity theorem of Fine and Wilf in the case of two relatively prime abelian periods and conjectured a result for the case of two non-relatively prime abelian periods. In this paper, we answer some open problems they suggested. We show that their conjecture is false but we give bounds, that depend on the two abelian periods, such that the conjecture is true for all words having length at least those bounds and show that some...

Advice Complexity and Barely Random Algorithms

Dennis Komm, Richard Královič (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization. Our...

Advice Complexity and Barely Random Algorithms

Dennis Komm, Richard Královič (2011)

RAIRO - Theoretical Informatics and Applications

Recently, a new measurement – the advice complexity – was introduced for measuring the information content of online problems. The aim is to measure the bitwise information that online algorithms lack, causing them to perform worse than offline algorithms. Among a large number of problems, a well-known scheduling problem, job shop scheduling with unit length tasks, and the paging problem were analyzed within this model. We observe some connections between advice complexity and randomization....

Algebra of Polynomially Bounded Sequences and Negligible Functions

Hiroyuki Okazaki (2015)

Formalized Mathematics

In this article we formalize negligible functions that play an essential role in cryptology [10], [2]. Generally, a cryptosystem is secure if the probability of succeeding any attacks against the cryptosystem is negligible. First, we formalize the algebra of polynomially bounded sequences [20]. Next, we formalize negligible functions and prove the set of negligible functions is a subset of the algebra of polynomially bounded sequences. Moreover, we then introduce equivalence relation between polynomially...

Algorithmes universels

Louis Nolin (1974)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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