We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of the output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request, and minimized over all algorithmoracle pairs) communicated by the algorithm to the oracle in order to solve the problem optimally. Hence, the advice complexity measures the amount of problem-relevant information contained in the input. We introduce two modes of communication between the algorithm and the oracle based on whether the oracle offers an advice spontaneously (helper) or on request (answerer). We analyze the Paging and DiffServ problems in terms of advice complexity and deliver upper and lower bounds in both communication modes; in the case of DiffServ problem in helper mode the bounds are tight.

We propose a new way of characterizing the complexity of online problems. Instead of measuring the degradation of output quality caused by the ignorance of the future we choose to quantify the amount of additional global information needed for an online algorithm to solve the problem optimally. In our model, the algorithm cooperates with an oracle that can see the whole input. We define the advice complexity of the problem to be the minimal number of bits (normalized per input request, and minimized over all algorithm-oracle pairs) communicated between the algorithm and the oracle in order to solve the problem optimally. Hence, the advice complexity measures the amount of problem-relevant information contained in the input.We introduce two modes of communication between the algorithm and the oracle based on whether the oracle offers an advice spontaneously (helper) or on request (answerer). We analyze the Paging and DiffServ problems in terms of advice complexity and deliver tight bounds in both communication modes.

The complexity of systolic dissemination of information in interconnection networks Informatique théorique et applications, tome 28, n o 3-4 (1994), p. 303-342 © AFCET, 1994, tous droits réservés. L'accès aux archives de la revue « Informatique théorique et applications » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Informatique théorique et Apphcations/Theoretical Informaties and Applications (vol 28, n° 3-4, 1994, p 303 à 342) THE COMPLEXITY OF SYSTOLIC DISSEMINATION OF INFORMATION IN INTERCONNECTION NETWORKS (1) by I HROMKOVIC (2) (4), R. KLASING (2), W. UNGER (2), H. WAGENER (2) (5) and D. PARDUBSKÂ (3) (6) Abstract-A concept of systohe dissémination of information in interconnection networks is presented, and the complexity of systohe gossip and broadeast in one-way (telegraph) and two-way (téléphone) communication mode is investigated The following main results are estabhshed (i) a gênerai relation between systohe broadeast and systohe gossip, (u) optimal systohe gossip algonthms on paths in both communication modes, and (m) optimal systohe gossip algonthms for complete k-ary trees in both communication modes

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