The Power of Dynamic Distance Oracles: Efficient Dynamic Algorithms for the Steiner Tree

In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good approximation of the minimum Steiner tree spanning a terminal set $S \subseteq V$, which changes over time. The changes applied to the terminal set are either terminal additions (incremental scenario), terminal removals (decremental scenario), or both (fully dynamic scenario). Our task here is twofold. We want to support updates in sublinear $o(n)$ time, and keep the approximation factor of the algorithm as small as possible. We show that we can maintain a $(6+\varepsilon)$-approximate Steiner tree of a general graph in $\tilde{O}(\sqrt{n} \log D)$ time per terminal addition or removal. Here, $D$ denotes the stretch of the metric induced by $G$. For planar graphs we achieve the same running time and the approximation ratio of $(2+\varepsilon)$. Moreover, we show faster algorithms for incremental and decremental scenarios. Finally, we show that if we allow higher approximation ratio, even more efficient algorithms are possible. In particular we show a polylogarithmic time $(4+\varepsilon)$-approximate algorithm for planar graphs. One of the main building blocks of our algorithms are dynamic distance oracles for vertex-labeled graphs, which are of independent interest. We also improve and use the online algorithms for the Steiner tree problem.Comment: Full version of the paper accepted to STOC'1

Asymptotically-Optimal Incentive-Based En-Route Caching Scheme

Content caching at intermediate nodes is a very effective way to optimize the operations of Computer networks, so that future requests can be served without going back to the origin of the content. Several caching techniques have been proposed since the emergence of the concept, including techniques that require major changes to the Internet architecture such as Content Centric Networking. Few of these techniques consider providing caching incentives for the nodes or quality of service guarantees for content owners. In this work, we present a low complexity, distributed, and online algorithm for making caching decisions based on content popularity, while taking into account the aforementioned issues. Our algorithm performs en-route caching. Therefore, it can be integrated with the current TCP/IP model. In order to measure the performance of any online caching algorithm, we define the competitive ratio as the ratio of the performance of the online algorithm in terms of traffic savings to the performance of the optimal offline algorithm that has a complete knowledge of the future. We show that under our settings, no online algorithm can achieve a better competitive ratio than $\Omega(\log n)$, where $n$ is the number of nodes in the network. Furthermore, we show that under realistic scenarios, our algorithm has an asymptotically optimal competitive ratio in terms of the number of nodes in the network. We also study an extension to the basic algorithm and show its effectiveness through extensive simulations

Sample Efficient Policy Search for Optimal Stopping Domains

Optimal stopping problems consider the question of deciding when to stop an observation-generating process in order to maximize a return. We examine the problem of simultaneously learning and planning in such domains, when data is collected directly from the environment. We propose GFSE, a simple and flexible model-free policy search method that reuses data for sample efficiency by leveraging problem structure. We bound the sample complexity of our approach to guarantee uniform convergence of policy value estimates, tightening existing PAC bounds to achieve logarithmic dependence on horizon length for our setting. We also examine the benefit of our method against prevalent model-based and model-free approaches on 3 domains taken from diverse fields.Comment: To appear in IJCAI-201