Kim S. Larsen

The relative worst-order ratio applied to paging

The relative worst order ratio, a new measure for the quality of on-line algorithms, was recently defined and applied to two bin packing problems. Here, we apply it to the paging problem and obtain the following results: We devise a new deterministic paging algorithm, Retrospective-LRU, and show that it performs better than LRU. This is supported by experimental results, but contrasts with the competitive ratio. All deterministic marking algorithms have the same competitive ratio, but here we find that LRU is better than FWF. According to the relative worst order ratio, no deterministic marking algorithm can be significantly better than LRU, but the randomized algorithm MARK is better than LRU. Finally, look-ahead is shown to be a significant advantage, in contrast to the competitive ratio, which does not reflect that look-ahead can be helpful.

The Accommodating Function: A Generalization of the Competitive Ratio

A new measure, the accommodating function, for the quality of on-line algorithms is presented. The accommodating function, which is a generalization of both the competitive ratio and the competitive ratio on accommodating sequences, measures the quality of an on-line algorithm as a function of the resources that would be sufficient for an optimal off-line algorithm to fully grant all requests. More precisely, if we have some amount of resources n, the function value at

Fully abstract models for a process language with refinement

\alpha

AVL trees with relaxed balance

is the usual ratio (still on some fixed amount of resources n), except that input sequences are restricted to those where the optimal off-line algorithm will not obtain a better result by having more than the amount

Amortization Results for Chromatic Search Trees, with an Application to Priority Queues

\alpha n

Online Bin Packing with Advice

of resources. The accommodating functions for three specific on-line problems are investigated: a variant of bin packing in which the goal is to maximize the number of items put in n bins, the seat reservation problem, and the problem of optimizing total flow time when preemption is allowed. We also show that when trying to distinguish between two algorithms, the decision as to which one performs better cannot necessarily be made from the competitive ratio or the competitive ratio on accommodating sequences alone. For the variant of bin-packing considered, we show that Worst-Fit has a strictly better competitive ratio than First-Fit, while First-Fit has a strictly better competitive ratio on accommodating sequences than Worst-Fit.

EFFICIENT REBALANCING OF B-TREES WITH RELAXED BALANCE

We study the use of sets of labelled partial orders (pomsets) as denotational models for process algebras. More specifically, we study their capability to capture degrees of nonsequentiality of processes. We present four full abstractness results. The operational equivalences are based on maximal action-sequences and step-sequences — defined for a very simple process language and its extensions with a refinement combinator (change of atomicity). The denotational models are all expressed as abstractions of a standard association of sets of labelled partial orders with processes.

Tight bounds on the competitive ratio on accommodating sequences for the seat reservation problem

AVL trees with relaxed balance (G.M. Adelson-Velskii et al., 1962) were introduced with the aim of improving runtime performance by allowing a greater degree of concurrency. This is obtained by uncoupling updating from rebalancing. We define a new collection of rebalancing operations which allows for a significantly greater degree of concurrency than the original proposal. Additionally, in contrast to the original proposal, we prove the complexity of the rebalancing. If N is the maximum size the tree could ever have, we prove that each insertion gives rise to at most /spl lsqb/log/sub /spl phi(N+3/2)+log/sub /spl phi(/spl radic/(5))/spl minus/3/spl rsqb/ rebalancing operations and that each deletion gives rise to at most /spl lsqb/log/sub /spl phi(N+3/2)+log/sub /spl phi(/spl radic/(5))/spl minus/4/spl rsqb/ rebalancing operations, where /spl phi/ is the golden ratio.<<ETX>>

Relaxed Balance through Standard Rotations

The intention in designing data structures with relaxed balance, such as chromatic search trees, is to facilitate fast updating on shared-memory asynchronous parallel architectures. To obtain this, the updating and rebalancing have been uncoupled, so extensive locking in connection with updates is avoided. In this paper, we prove that only an amortized constant amount of rebalancing is necessary after an update in a chromatic search tree. We also prove that the amount of rebalancing done at any particular level decreases exponentially, going from the leaves toward the root. These results imply that, in principle, a linear number of processes can access the tree simultaneously. We have included one interesting application of chromatic trees. Based on these trees, a priority queue with possibilities for a greater degree of parallelism than previous proposals can be implemented.

Amortized Constant Relaxed Rebalancing using Standard Rotations

We consider the online bin packing problem under the advice complexity model where the “online constraint” is relaxed and an algorithm receives partial information about the future items. We provide tight upper and lower bounds for the amount of advice an algorithm needs to achieve an optimal packing. We also introduce an algorithm that, when provided with