Optimal competitiveness for Symmetric Rectilinear Steiner Arborescence and related problems

We present optimal competitive algorithms for two interrelated known problems involving Steiner Arborescence. One is the continuous problem of the Symmetric Rectilinear Steiner Arborescence (SRSA), studied by Berman and Coulston. A very related, but discrete problem (studied separately in the past) is the online Multimedia Content Delivery (MCD) problem on line networks, presented originally by Papadimitriu, Ramanathan, and Rangan. An efficient content delivery was modeled as a low cost Steiner arborescence in a grid of network*time they defined. We study here the version studied by Charikar, Halperin, and Motwani (who used the same problem definitions, but removed some constraints on the inputs). The bounds on the competitive ratios introduced separately in the above papers are similar for the two problems: O(log N) for the continuous problem and O(log n) for the network problem, where N was the number of terminals to serve, and n was the size of the network. The lower bounds were Omega(sqrt{log N}) and Omega(sqrt{log n}) correspondingly. Berman and Coulston conjectured that both the upper bound and the lower bound could be improved. We disprove this conjecture and close these quadratic gaps for both problems. We first present an O(sqrt{log n}) deterministic competitive algorithm for MCD on the line, matching the lower bound. We then translate this algorithm to become a competitive optimal algorithm O(sqrt{log N}) for SRSA. Finally, we translate the latter back to solve MCD problem, this time competitive optimally even in the case that the number of requests is small (that is, O(min{sqrt{log n},sqrt{log N}})). We also present a Omega(sqrt[3]{log n}) lower bound on the competitiveness of any randomized algorithm. Some of the techniques may be useful in other contexts

Optimal competitiveness for the Rectilinear Steiner Arborescence problem

We present optimal online algorithms for two related known problems involving Steiner Arborescence, improving both the lower and the upper bounds. One of them is the well studied continuous problem of the {\em Rectilinear Steiner Arborescence} ($RSA$). We improve the lower bound and the upper bound on the competitive ratio for $RSA$ from $O(\log N)$ and $\Omega(\sqrt{\log N})$ to $\Theta(\frac{\log N}{\log \log N})$, where $N$ is the number of Steiner points. This separates the competitive ratios of $RSA$ and the Symetric-$RSA$, two problems for which the bounds of Berman and Coulston is STOC 1997 were identical. The second problem is one of the Multimedia Content Distribution problems presented by Papadimitriou et al. in several papers and Charikar et al. SODA 1998. It can be viewed as the discrete counterparts (or a network counterpart) of $RSA$. For this second problem we present tight bounds also in terms of the network size, in addition to presenting tight bounds in terms of the number of Steiner points (the latter are similar to those we derived for $RSA$)

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Across Space and Time. Papers from the 41st Conference on Computer Applications and Quantitative Methods in Archaeology, Perth, 25-28 March 2013

This volume presents a selection of the best papers presented at the forty-first annual Conference on Computer Applications and Quantitative Methods in Archaeology. The theme for the conference was "Across Space and Time", and the papers explore a multitude of topics related to that concept, including databases, the semantic Web, geographical information systems, data collection and management, and more

Across Space and Time Papers from the 41st Conference on Computer Applications and Quantitative Methods in Archaeology, Perth, 25-28 March 2013

The present volume includes 50 selected peer-reviewed papers presented at the 41st Computer Applications and Quantitative Methods in Archaeology Across Space and Time (CAA2013) conference held in Perth (Western Australia) in March 2013 at the University Club of Western Australia and hosted by the recently established CAA Australia National Chapter. It also hosts a paper presented at the 40th Computer Applications and Quantitative Methods in Archaeology (CAA2012) conference held in Southampton