A Simple Deterministic Distributed MST Algorithm, with Near-Optimal Time and Message Complexities

Distributed minimum spanning tree (MST) problem is one of the most central and fundamental problems in distributed graph algorithms. Garay et al. \cite{GKP98,KP98} devised an algorithm with running time $O(D + \sqrt{n} \cdot \log^* n)$, where $D$ is the hop-diameter of the input $n$-vertex $m$-edge graph, and with message complexity $O(m + n^{3/2})$. Peleg and Rubinovich \cite{PR99} showed that the running time of the algorithm of \cite{KP98} is essentially tight, and asked if one can achieve near-optimal running time **together with near-optimal message complexity**. In a recent breakthrough, Pandurangan et al. \cite{PRS16} answered this question in the affirmative, and devised a **randomized** algorithm with time $\tilde{O}(D+ \sqrt{n})$ and message complexity $\tilde{O}(m)$. They asked if such a simultaneous time- and message-optimality can be achieved by a **deterministic** algorithm. In this paper, building upon the work of \cite{PRS16}, we answer this question in the affirmative, and devise a **deterministic** algorithm that computes MST in time $O((D + \sqrt{n}) \cdot \log n)$, using $O(m \cdot \log n + n \log n \cdot \log^* n)$ messages. The polylogarithmic factors in the time and message complexities of our algorithm are significantly smaller than the respective factors in the result of \cite{PRS16}. Also, our algorithm and its analysis are very **simple** and self-contained, as opposed to rather complicated previous sublinear-time algorithms \cite{GKP98,KP98,E04b,PRS16}

Tradeoffs in worst-case equilibria

AbstractWe investigate the problem of routing traffic through a congested network in an environment of non-cooperative users. We use the worst-case coordination ratio suggested by Koutsoupias and Papadimitriou to measure the performance degradation due to the lack of a centralized traffic regulating authority. We provide a full characterization of the worst-case coordination ratio in the restricted assignment and unrelated parallel links model. In particular, we quantify the tradeoff between the “negligibility” of the traffic controlled by each user and the worst-case coordination ratio. We analyze both pure and mixed strategies systems and identify the range where their performance is similar

The maintenance of common data in a distributed system

A basic task in distributed computation is the maintenance at each processor of the network, of a current and accurate copy of a common database. A primary example is the maintenance, for routing and other purposes, of a record of the current topology of the system. Such a database must be updated in the wake of locally generated changes to its contents. Due to previous disconnections of parts of the network, a maintenance protocol may need to update processors holding widely varying versions of the database. We provide a deterministic protocol for this problem, which has only polylogarithmic overhead in its time and communication complexities. Previous deterministic solutions required polynomial overhead in at least one of these measures

Reducing truth-telling online mechanisms to online optimization

Abstract We describe a general technique for converting an online algorithm B to a truthtelling mechanism. We require that theoriginal online competitive algorithm has certain "niceness " properties in that actions on future requests are independent of the actual value of requests which were accepted (though these actions will of course depend upon the set of acceptedrequests). Under these conditions, we are able to give an online truth telling mechanism (where the values of requests are given by bids which may not accurately represent the valuation of the requesters) such that our total profit is within O(ae + log _) of the optimum offline profit obtained by an omniscient algorithm (one which knows the true valuationsof the users). Here ae is the competitive ratio of B for the optimization version of the problem, and _ is the ratio of themaximum to minimum valuation for a request. In general there is an \Omega (log _) lower bound on the ratio of worst-case profitfor a truth telling mechanism when compared to the profit obtained by an omniscient algorithm, so this result is in som