Self-adjusting Tree Research Articles

Randomized distributed self-adjusting tree networks

In this paper we investigate the benefits of randomization in the design of self-adjusting network topologies: networks that dynamically adapt themselves toward the demand they currently serve, in an online manner. We present a randomized self-adjusting tree network, which leverages randomization to reduce the expected network reconfiguration cost by a constant factor, compared to existing deterministic solutions. The new solution is simple, easy-to-implement, fully distributed and concurrent. We prove algorithm correctness, provide expected amortized cost limits, and present simulation results on workloads with variable spatial and temporal complexity.

Distributed Self-Adjusting Tree Networks

The performance of many data-centric cloud applications critically depends on the performance of the underlying datacenter network. Reconfigurable optical technologies have recently introduced a novel opportunity to improve datacenter network performance, by allowing to dynamically adjust the network topology according to the demand. However, the vision of self-adjusting networks raises the fundamental question how such networks can be efficiently operated in a scalable and distributed manner. This article presents <inline-formula><tex-math notation="LaTeX">$DiSplayNet$</tex-math></inline-formula> , the first fully distributed self-adjusting network. <inline-formula><tex-math notation="LaTeX">$DiSplayNet$</tex-math></inline-formula> relies on algorithms that perform decentralized and concurrent topological adjustments to account for changes in the demand. We propose two natural metrics to evaluate the performance of distributed self-adjusting networks, the <i>amortized work</i> (the cost of routing on and adjusting the network) and the <i>makespan</i> (the time it takes to serve a set of communication requests). We present a rigorous formal analysis of the work and makespan of <inline-formula><tex-math notation="LaTeX">$DiSplayNet$</tex-math></inline-formula> , which can be seen as an interesting generalization of analyses known from sequential self-adjusting datastructures. We complement our theoretical contribution with an extensive trace-driven simulation study, shedding light on the opportunities and limitations of leveraging spatial and temporal locality and concurrency in self-adjusting networks.

Push-Down Trees: Optimal Self-Adjusting Complete Trees

This paper studies a fundamental algorithmic problem related to the design of demand-aware networks: networks whose topologies adjust toward the traffic patterns they serve, in an online manner. The goal is to strike a tradeoff between the benefits of such adjustments (shorter routes) and their costs (reconfigurations). In particular, we consider the problem of designing a self-adjusting tree network which serves single-source, multi-destination communication. The problem is a central building block for more general self-adjusting network designs and has interesting connections to self-adjusting datastructures. We present two constant-competitive online algorithms for this problem, one randomized and one deterministic. Our approach is based on a natural notion of Most Recently Used (MRU) tree, maintaining a working set. We prove that the working set is a cost lower bound for any online algorithm, and then present a randomized algorithm RANDOM- PUSH which approximates such an MRU tree at low cost, by pushing less recently used communication partners down the tree, along a random walk. Our deterministic algorithm Move-Half does not directly maintain an MRU tree, but its cost is still proportional to the cost of an MRU tree, and also matches the working set lower bound.

The Impact of Communication Patterns on Distributed Self-Adjusting Binary Search Tree

This paper introduces the problem of communication pattern adaption for a distributed self-adjusting binary search tree. We propose a simple local algorithm that is closely related to the over thirty-year-old idea of splay trees and evaluate its adaption performance in the distributed scenario if different communication patterns are provided. To do so, the process of self-adjustment is modeled similarly to a basic network creation game in which the nodes want to communicate with only a certain subset of all nodes. We show that, in general, the game (i.e., the process of local adjustments) does not converge, and that convergence is related to certain structures of the communication interests, which we call conflicts. We classify conflicts and show that for two communication scenarios in which convergence is guaranteed, the self-adjusting tree performs well. Furthermore, we investigate the different classes of conflicts separately and show that, for a certain class of conflicts, the performance of the tree network is asymptotically as good as the performance for converging instances. However, for the other conflict classes, a distributed self-adjusting binary search tree adapts poorly.

Optimizing Searching with Self-Adjusting Trees

Abstract Self-adjusting trees are data structures that modify their own structure to reflect the probabilistic nature of access patterns. The splay tree of Tarjan and Sleator performs tree operations in amortized O(log n) time. The splay operation moves an accessed node all the way to the root of the tree, and thus may not be the most efficient type of self-adjustment. In this paper several variations of the splay tree are described. Simulations are used to compare the optimality of the searches done by these trees for various patterns of data access.