Multicast Network Design Game on a Ring

In this paper we study quality measures of different solution concepts for the multicast network design game on a ring topology. We recall from the literature a lower bound of 4/3 and prove a matching upper bound for the price of stability, which is the ratio of the social costs of a best Nash equilibrium and of a general optimum. Therefore, we answer an open question posed by Fanelli et al. in [12]. We prove an upper bound of 2 for the ratio of the costs of a potential optimizer and of an optimum, provide a construction of a lower bound, and give a computer-assisted argument that it reaches $2$ for any precision. We then turn our attention to players arriving one by one and playing myopically their best response. We provide matching lower and upper bounds of 2 for the myopic sequential price of anarchy (achieved for a worst-case order of the arrival of the players). We then initiate the study of myopic sequential price of stability and for the multicast game on the ring we construct a lower bound of 4/3, and provide an upper bound of 26/19. To the end, we conjecture and argue that the right answer is 4/3.Comment: 12 pages, 4 figure

Entropy, Triangulation, and Point Location in Planar Subdivisions

A data structure is presented for point location in connected planar subdivisions when the distribution of queries is known in advance. The data structure has an expected query time that is within a constant factor of optimal. More specifically, an algorithm is presented that preprocesses a connected planar subdivision G of size n and a query distribution D to produce a point location data structure for G. The expected number of point-line comparisons performed by this data structure, when the queries are distributed according to D, is H + O(H^{2/3}+1) where H=H(G,D) is a lower bound on the expected number of point-line comparisons performed by any linear decision tree for point location in G under the query distribution D. The preprocessing algorithm runs in O(n log n) time and produces a data structure of size O(n). These results are obtained by creating a Steiner triangulation of G that has near-minimum entropy.Comment: 19 pages, 4 figures, lots of formula

Captain J. A. Macarthur Onslow walking by a building, New South Wales, 25 July 1930, 1 [picture].

Title devised from accompanying information where available.; Part of the: Fairfax archive of glass plate negatives.; Fairfax number: 2402.; Condition: silvering.; Also available online at: http://nla.gov.au/nla.pic-vn6192335; Acquired from Fairfax Media, 2012

Off-line admission control for advance reservations in star networks

Given a network together with a set of connection requests, call admission control is the problem of deciding which calls to accept and which ones to reject in order to maximize the total profit of the accepted requests. We consider call admission control problems with advance reservations in star networks. For the most general variant we present a constant-factor approximation algorithm resolving an open problem due to Erlebach. Our method is randomized and achieves an approximation ratio of 1/18. It can be generalized to accommodate call alternatives, in which case the approximation ratio is 1/24. We show how our method can be derandomized. In addition we prove that call admission control in star networks is -hard even for very restricted variants of the problem

Routing and Call Control Algorithms for Ring Networks

A vast majority of communications in a network occurs between pairs of nodes, each such interaction is termed a call. The job of call control algorithm is to decide which of a set of calls to accept in the network so as to maximize a certain objective, viz., the number of accepted calls or the profit associated with the accepted calls. When a call is accepted it uses up some network resources, like bandwidth, along the path through which it is routed. Thus, the call control algorithm needs to make intelligent trade-offs between resource constraints and profits. In this paper, we investigate two variants of call control problems on ring networks; in the first, the algorithm is allowed to determine the route connecting the end nodes of a call, while in the second, the route is specified as part of the input. For the first variant, we show an efficient algorithm that achieves the objective of routing and maximizing the nrnber of accepted calls within an additive constant of at most 3 to an optimal algorithm. This yields by-product. For the fixed path variant, we derive a 2-approximation for maximizing the profits (which could be arbitrary) of accepted calls