A Lightweight Distributed Solution to Content Replication in Mobile Networks

Performance and reliability of content access in mobile networks is conditioned by the number and location of content replicas deployed at the network nodes. Facility location theory has been the traditional, centralized approach to study content replication: computing the number and placement of replicas in a network can be cast as an uncapacitated facility location problem. The endeavour of this work is to design a distributed, lightweight solution to the above joint optimization problem, while taking into account the network dynamics. In particular, we devise a mechanism that lets nodes share the burden of storing and providing content, so as to achieve load balancing, and decide whether to replicate or drop the information so as to adapt to a dynamic content demand and time-varying topology. We evaluate our mechanism through simulation, by exploring a wide range of settings and studying realistic content access mechanisms that go beyond the traditional assumptionmatching demand points to their closest content replica. Results show that our mechanism, which uses local measurements only, is: (i) extremely precise in approximating an optimal solution to content placement and replication; (ii) robust against network mobility; (iii) flexible in accommodating various content access patterns, including variation in time and space of the content demand.Comment: 12 page

Incremental Medians via Online Bidding

In the k-median problem we are given sets of facilities and customers, and distances between them. For a given set F of facilities, the cost of serving a customer u is the minimum distance between u and a facility in F. The goal is to find a set F of k facilities that minimizes the sum, over all customers, of their service costs. Following Mettu and Plaxton, we study the incremental medians problem, where k is not known in advance, and the algorithm produces a nested sequence of facility sets where the kth set has size k. The algorithm is c-cost-competitive if the cost of each set is at most c times the cost of the optimum set of size k. We give improved incremental algorithms for the metric version: an 8-cost-competitive deterministic algorithm, a 2e ~ 5.44-cost-competitive randomized algorithm, a (24+epsilon)-cost-competitive, poly-time deterministic algorithm, and a (6e+epsilon ~ .31)-cost-competitive, poly-time randomized algorithm. The algorithm is s-size-competitive if the cost of the kth set is at most the minimum cost of any set of size k, and has size at most s k. The optimal size-competitive ratios for this problem are 4 (deterministic) and e (randomized). We present the first poly-time O(log m)-size-approximation algorithm for the offline problem and first poly-time O(log m)-size-competitive algorithm for the incremental problem. Our proofs reduce incremental medians to the following online bidding problem: faced with an unknown threshold T, an algorithm submits "bids" until it submits a bid that is at least the threshold. It pays the sum of all its bids. We prove that folklore algorithms for online bidding are optimally competitive.Comment: conference version appeared in LATIN 2006 as "Oblivious Medians via Online Bidding

Robust Legged Robot State Estimation Using Factor Graph Optimization

Legged robots, specifically quadrupeds, are becoming increasingly attractive for industrial applications such as inspection. However, to leave the laboratory and to become useful to an end user requires reliability in harsh conditions. From the perspective of state estimation, it is essential to be able to accurately estimate the robot's state despite challenges such as uneven or slippery terrain, textureless and reflective scenes, as well as dynamic camera occlusions. We are motivated to reduce the dependency on foot contact classifications, which fail when slipping, and to reduce position drift during dynamic motions such as trotting. To this end, we present a factor graph optimization method for state estimation which tightly fuses and smooths inertial navigation, leg odometry and visual odometry. The effectiveness of the approach is demonstrated using the ANYmal quadruped robot navigating in a realistic outdoor industrial environment. This experiment included trotting, walking, crossing obstacles and ascending a staircase. The proposed approach decreased the relative position error by up to 55% and absolute position error by 76% compared to kinematic-inertial odometry.Comment: 8 pages, 12 figures. Accepted to RA-L + IROS 2019, July 201

A taxonomy for emergency service station location problem

The emergency service station (ESS) location problem has been widely studied in the literature since 1970s. There has been a growing interest in the subject especially after 1990s. Various models with different objective functions and constraints have been proposed in the academic literature and efficient solution techniques have been developed to provide good solutions in reasonable times. However, there is not any study that systematically classifies different problem types and methodologies to address them. This paper presents a taxonomic framework for the ESS location problem using an operations research perspective. In this framework, we basically consider the type of the emergency, the objective function, constraints, model assumptions, modeling, and solution techniques. We also analyze a variety of papers related to the literature in order to demonstrate the effectiveness of the taxonomy and to get insights for possible research directions

Reallocating Multiple Facilities on the Line

We study the multistage $K$-facility reallocation problem on the real line, where we maintain $K$ facility locations over $T$ stages, based on the stage-dependent locations of $n$ agents. Each agent is connected to the nearest facility at each stage, and the facilities may move from one stage to another, to accommodate different agent locations. The objective is to minimize the connection cost of the agents plus the total moving cost of the facilities, over all stages. $K$-facility reallocation was introduced by de Keijzer and Wojtczak, where they mostly focused on the special case of a single facility. Using an LP-based approach, we present a polynomial time algorithm that computes the optimal solution for any number of facilities. We also consider online $K$-facility reallocation, where the algorithm becomes aware of agent locations in a stage-by-stage fashion. By exploiting an interesting connection to the classical $K$-server problem, we present a constant-competitive algorithm for $K = 2$ facilities

Efficient Approximation Schemes for Uniform-Cost Clustering Problems in Planar Graphs

We consider the k-Median problem on planar graphs: given an edge-weighted planar graph G, a set of clients C subseteq V(G), a set of facilities F subseteq V(G), and an integer parameter k, the task is to find a set of at most k facilities whose opening minimizes the total connection cost of clients, where each client contributes to the cost with the distance to the closest open facility. We give two new approximation schemes for this problem: - FPT Approximation Scheme: for any epsilon>0, in time 2^{O(k epsilon^{-3} log (k epsilon^{-1}))}* n^O(1) we can compute a solution that has connection cost at most (1+epsilon) times the optimum, with high probability. - Efficient Bicriteria Approximation Scheme: for any epsilon>0, in time 2^{O(epsilon^{-5} log (epsilon^{-1}))}* n^O(1) we can compute a set of at most (1+epsilon)k facilities whose opening yields connection cost at most (1+epsilon) times the optimum connection cost for opening at most k facilities, with high probability. As a direct corollary of the second result we obtain an EPTAS for Uniform Facility Location on planar graphs, with same running time. Our main technical tool is a new construction of a "coreset for facilities" for k-Median in planar graphs: we show that in polynomial time one can compute a subset of facilities F_0 subseteq F of size k * (log n/epsilon)^O(epsilon^{-3}) with a guarantee that there is a (1+epsilon)-approximate solution contained in F_0

Algebraic solution to a constrained rectilinear minimax location problem on the plane

We consider a constrained minimax single facility location problem on the plane with rectilinear distance. The feasible set of location points is restricted to rectangles with sides oriented at a 45 degrees angle to the axes of Cartesian coordinates. To solve the problem, an algebraic approach based on an extremal property of eigenvalues of irreducible matrices in idempotent algebra is applied. A new algebraic solution is given that reduces the problem to finding eigenvalues and eigenvectors of appropriately defined matrices.Comment: 2011 International Conference on Multimedia Technology (ICMT), 26-28 July 2011, Hangzhou, China. ISBN 978-1-61284-771-