The Stochastic Bottleneck Linear Programming Problem

In this paper we consider some stochastic bottleneck linear prograrnming problems. In the case when the coefficients of the objective functions are simple randomized, the minimum-risk approach will be used for solving these problems. We prove that, under some positivity conditions, these stochastic problems are reduced to certain deterministic bottleneck linear problems. Applications of these problems to the bottleneck spanning tree problems and bottleneck investment allocation problems are given. A simple numerical example is presented

Restricted Dynamic Programming Heuristic for Precedence Constrained Bottleneck Generalized TSP

We develop a restricted dynamical programming heuristic for a complicated traveling salesman problem: a) cities are grouped into clusters, resp. Generalized TSP; b) precedence constraints are imposed on the order of visiting the clusters, resp. Precedence Constrained TSP; c) the costs of moving to the next cluster and doing the required job inside one are aggregated in a minimax manner, resp. Bottleneck TSP; d) all the costs may depend on the sequence of previously visited clusters, resp. Sequence-Dependent TSP or Time Dependent TSP. Such multiplicity of constraints complicates the use of mixed integer-linear programming, while dynamic programming (DP) benefits from them; the latter may be supplemented with a branch-and-bound strategy, which necessitates a “DP-compliant” heuristic. The proposed heuristic always yields a feasible solution, which is not always the case with heuristics, and its precision may be tuned until it becomes the exact DP

Train Scheduling and Rescheduling in the UK with a Modified Shifting Bottleneck Procedure

This paper introduces a modified shifting bottleneck approach to solve train scheduling and rescheduling problems. The problem is formulated as a job shop scheduling model and a mixed integer linear programming model is also presented. The shifting bottleneck procedure is a well-established heuristic method for obtaining solutions to the job shop and other machine scheduling problems. We modify the classical shifting bottleneck approach to make it suitable for the types of job shop problem that arises in train scheduling. The method decomposes the problem into several single machine problems. Different variations of the method are considered with regard to solving the single machine problems. We compare and report the performance of the algorithms for a case study based on part of the UK railway network

Trajectory Aware Macro-cell Planning for Mobile Users

We design and evaluate algorithms for efficient user-mobility driven macro-cell planning in cellular networks. As cellular networks embrace heterogeneous technologies (including long range 3G/4G and short range WiFi, Femto-cells, etc.), most traffic generated by static users gets absorbed by the short-range technologies, thereby increasingly leaving mobile user traffic to macro-cells. To this end, we consider a novel approach that factors in the trajectories of mobile users as well as the impact of city geographies and their associated road networks for macro-cell planning. Given a budget k of base-stations that can be upgraded, our approach selects a deployment that impacts the most number of user trajectories. The generic formulation incorporates the notion of quality of service of a user trajectory as a parameter to allow different application-specific requirements, and operator choices.We show that the proposed trajectory utility maximization problem is NP-hard, and design multiple heuristics. We evaluate our algorithms with real and synthetic data sets emulating different city geographies to demonstrate their efficacy. For instance, with an upgrade budget k of 20%, our algorithms perform 3-8 times better in improving the user quality of service on trajectories in different city geographies when compared to greedy location-based base-station upgrades.Comment: Published in INFOCOM 201

Improved Finite Blocklength Converses for Slepian-Wolf Coding via Linear Programming

A new finite blocklength converse for the Slepian- Wolf coding problem is presented which significantly improves on the best known converse for this problem, due to Miyake and Kanaya [2]. To obtain this converse, an extension of the linear programming (LP) based framework for finite blocklength point- to-point coding problems from [3] is employed. However, a direct application of this framework demands a complicated analysis for the Slepian-Wolf problem. An analytically simpler approach is presented wherein LP-based finite blocklength converses for this problem are synthesized from point-to-point lossless source coding problems with perfect side-information at the decoder. New finite blocklength metaconverses for these point-to-point problems are derived by employing the LP-based framework, and the new converse for Slepian-Wolf coding is obtained by an appropriate combination of these converses.Comment: under review with the IEEE Transactions on Information Theor