Quantifying the benefits of vehicle pooling with shareability networks

Taxi services are a vital part of urban transportation, and a considerable contributor to traffic congestion and air pollution causing substantial adverse effects on human health. Sharing taxi trips is a possible way of reducing the negative impact of taxi services on cities, but this comes at the expense of passenger discomfort quantifiable in terms of a longer travel time. Due to computational challenges, taxi sharing has traditionally been approached on small scales, such as within airport perimeters, or with dynamical ad-hoc heuristics. However, a mathematical framework for the systematic understanding of the tradeoff between collective benefits of sharing and individual passenger discomfort is lacking. Here we introduce the notion of shareability network which allows us to model the collective benefits of sharing as a function of passenger inconvenience, and to efficiently compute optimal sharing strategies on massive datasets. We apply this framework to a dataset of millions of taxi trips taken in New York City, showing that with increasing but still relatively low passenger discomfort, cumulative trip length can be cut by 40% or more. This benefit comes with reductions in service cost, emissions, and with split fares, hinting towards a wide passenger acceptance of such a shared service. Simulation of a realistic online system demonstrates the feasibility of a shareable taxi service in New York City. Shareability as a function of trip density saturates fast, suggesting effectiveness of the taxi sharing system also in cities with much sparser taxi fleets or when willingness to share is low.Comment: Main text: 6 pages, 3 figures, SI: 24 page

Improving information centrality of a node in complex networks by adding edges

The problem of increasing the centrality of a network node arises in many practical applications. In this paper, we study the optimization problem of maximizing the information centrality $I_v$ of a given node $v$ in a network with $n$ nodes and $m$ edges, by creating $k$ new edges incident to $v$. Since $I_v$ is the reciprocal of the sum of resistance distance $\mathcal{R}_v$ between $v$ and all nodes, we alternatively consider the problem of minimizing $\mathcal{R}_v$ by adding $k$ new edges linked to $v$. We show that the objective function is monotone and supermodular. We provide a simple greedy algorithm with an approximation factor $\left(1-\frac{1}{e}\right)$ and $O(n^3)$ running time. To speed up the computation, we also present an algorithm to compute $\left(1-\frac{1}{e}-\epsilon\right)$-approximate resistance distance $\mathcal{R}_v$ after iteratively adding $k$ edges, the running time of which is $\widetilde{O} (mk\epsilon^{-2})$ for any $\epsilon>0$, where the $\widetilde{O} (\cdot)$ notation suppresses the ${\rm poly} (\log n)$ factors. We experimentally demonstrate the effectiveness and efficiency of our proposed algorithms.Comment: 7 pages, 2 figures, ijcai-201

Distributed Approximation of Maximum Independent Set and Maximum Matching

We present a simple distributed $\Delta$-approximation algorithm for maximum weight independent set (MaxIS) in the $\mathsf{CONGEST}$ model which completes in $O(\texttt{MIS}(G)\cdot \log W)$ rounds, where $\Delta$ is the maximum degree, $\texttt{MIS}(G)$ is the number of rounds needed to compute a maximal independent set (MIS) on $G$, and $W$ is the maximum weight of a node. %Whether our algorithm is randomized or deterministic depends on the \texttt{MIS} algorithm used as a black-box. Plugging in the best known algorithm for MIS gives a randomized solution in $O(\log n \log W)$ rounds, where $n$ is the number of nodes. We also present a deterministic $O(\Delta +\log^* n)$-round algorithm based on coloring. We then show how to use our MaxIS approximation algorithms to compute a $2$-approximation for maximum weight matching without incurring any additional round penalty in the $\mathsf{CONGEST}$ model. We use a known reduction for simulating algorithms on the line graph while incurring congestion, but we show our algorithm is part of a broad family of \emph{local aggregation algorithms} for which we describe a mechanism that allows the simulation to run in the $\mathsf{CONGEST}$ model without an additional overhead. Next, we show that for maximum weight matching, relaxing the approximation factor to ($2+\varepsilon$) allows us to devise a distributed algorithm requiring $O(\frac{\log \Delta}{\log\log\Delta})$ rounds for any constant $\varepsilon>0$. For the unweighted case, we can even obtain a $(1+\varepsilon)$-approximation in this number of rounds. These algorithms are the first to achieve the provably optimal round complexity with respect to dependency on $\Delta$

A Faster Distributed Single-Source Shortest Paths Algorithm

We devise new algorithms for the single-source shortest paths (SSSP) problem with non-negative edge weights in the CONGEST model of distributed computing. While close-to-optimal solutions, in terms of the number of rounds spent by the algorithm, have recently been developed for computing SSSP approximately, the fastest known exact algorithms are still far away from matching the lower bound of $\tilde \Omega (\sqrt{n} + D)$ rounds by Peleg and Rubinovich [SIAM Journal on Computing 2000], where $n$ is the number of nodes in the network and $D$ is its diameter. The state of the art is Elkin's randomized algorithm [STOC 2017] that performs $\tilde O(n^{2/3} D^{1/3} + n^{5/6})$ rounds. We significantly improve upon this upper bound with our two new randomized algorithms for polynomially bounded integer edge weights, the first performing $\tilde O (\sqrt{n D})$ rounds and the second performing $\tilde O (\sqrt{n} D^{1/4} + n^{3/5} + D)$ rounds. Our bounds also compare favorably to the independent result by Ghaffari and Li [STOC 2018]. As side results, we obtain a $(1 + \epsilon)$-approximation $\tilde O ((\sqrt{n} D^{1/4} + D) / \epsilon)$-round algorithm for directed SSSP and a new work/depth trade-off for exact SSSP on directed graphs in the PRAM model.Comment: Presented at the the 59th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2018

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed