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Factor frequencies in generalized Thue-Morse words

Ľubomíra Balková (2012)

Kybernetika

We describe factor frequencies of the generalized Thue-Morse word 𝐭 b , m defined for b 2 , m 1 , b , m , as the fixed point starting in 0 of the morphism ϕ b , m ( k ) = k ( k + 1 ) ( k + b - 1 ) , where k { 0 , 1 , , m - 1 } and where the letters are expressed modulo m . We...

Factoring and testing primes in small space

Viliam Geffert, Dana Pardubská (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We discuss how much space is sufficient to decide whether a unary given number n is a prime. We show that O(log log n) space is sufficient for a deterministic Turing machine, if it is equipped with an additional pebble movable along the input tape, and also for an alternating machine, if the space restriction applies only to its accepting computation subtrees. In other words, the language is a prime is in pebble–DSPACE(log log n) and also in accept–ASPACE(log log n). Moreover, if the given n is...

Fast approximation of minimum multicast congestion – Implementation versus theory

Andreas Baltz, Anand Srivastav (2004)

RAIRO - Operations Research - Recherche Opérationnelle

The problem of minimizing the maximum edge congestion in a multicast communication network generalizes the well-known N P -hard multicommodity flow problem. We give the presently best theoretical approximation results as well as efficient implementations. In particular we show that for a network with m edges and k multicast requests, an r ( 1 + ε ) ( r t e x t O P T + exp ( 1 ) ln m ) -approximation can be computed in O ( k m ε - 2 ln k ln m ) time, where β bounds the time for computing an r -approximate minimum Steiner tree. Moreover, we present a new fast heuristic that...

Fast approximation of minimum multicast congestion – Implementation VERSUS Theory

Andreas Baltz, Anand Srivastav (2010)

RAIRO - Operations Research

The problem of minimizing the maximum edge congestion in a multicast communication network generalizes the well-known NP-hard multicommodity flow problem. We give the presently best theoretical approximation results as well as efficient implementations. In particular we show that for a network with m edges and k multicast requests, an r(1 + ε)(rOPT + exp(1)lnm)-approximation can be computed in O(kmε-2lnklnm) time, where β bounds the time for computing an r-approximate minimum Steiner tree. Moreover,...

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