Sushmita Gupta

Access graphs results for LRU versus FIFO under relative worst order analysis

Access graphs, which have been used previously in connection with competitive analysis to model locality of reference in paging, are considered in connection with relative worst order analysis. In this model, FWF is shown to be strictly worse than both LRU and FIFO on any access graph. LRU is shown to be strictly better than FIFO on paths and cycles, but they are incomparable on some families of graphs which grow with the length of the sequences.

On the Advice Complexity of the k-server Problem Under Sparse Metrics

We consider the k-Server problem under the advice model of computation when the underlying metric space is sparse. On one side, we introduce Θ(1)-competitive algorithms for a wide range of sparse graphs. These algorithms require advice of (almost) linear size. We show that for graphs of size N and treewidth α, there is an online algorithm that receives O (n(log α + log log N))* bits of advice and optimally serves any sequence of length n. We also prove that if a graph admits a system of μ collective tree (q, r)-spanners, then there is a (q + r)-competitive algorithm which requires O (n(log μ + log log N)) bits of advice. Among other results, this gives a 3-competitive algorithm for planar graphs, when provided with O (n log log N) bits of advice. On the other side, we prove that advice of size Ω(n) is required to obtain a 1-competitive algorithm for sequences of length n even for the 2-server problem on a path metric of size N ≥ 3. Through another lower bound argument, we show that at least n2(logα−1.22)

Relative interval analysis of paging algorithms on access graphs

\frac {n}{2}(\log \alpha - 1.22)

Parameterized algorithms for stable matching with ties and incomplete lists

bits of advice is required to obtain an optimal solution for metric spaces of treewidth α, where 4 ≤ α < 2k.

Total Stability in Stable Matching Games.

Access graphs, which have been used previously in connection to competitive analysis and relative worst order analysis to model locality of reference in paging, are considered in connection with relative interval analysis. The algorithms LRU, FIFO, FWF, and FAR are compared using the path, star, and cycle access graphs. In this model, some of the results obtained are not surprising. However, although LRU is found to be strictly better than FIFO on paths, it has worse performance on stars, cycles, and complete graphs, in this model. We solve an open question from Dorrigiv et al. (2009) 13], obtaining tight bounds on the relationship between LRU and FIFO with relative interval analysis.

Stable Nash Equilibria in the Gale-Shapley Matching Game.

Abstract We study the parameterized complexity of NP-hard optimization versions of Stable Matching and Stable Roommates in the presence of ties and incomplete lists. These problems model many real-life situations where solutions have to satisfy certain predefined criterion of suitability and compatibility. Specifically, our objective is to maximize/minimize the size of the stable matching. Our main theorems state that Stable Matching and Stable Roommates admit small kernels. Consequently, we also conclude that Stable Matching is fixed-parameter tractable ( FPT ) with respect to solution size, and that Stable Roommates is FPT with respect to a structural parameter. Finally, we analyze the special case where the input graph is planar.