Finding a length-constrained maximum-sum or maximum-density subtree and its application to logistics

AbstractWe study the problem of finding a length-constrained maximum-density path in a tree with weight and length on each edge. This problem was proposed in [R.R. Lin, W.H. Kuo, K.M. Chao, Finding a length-constrained maximum-density path in a tree, Journal of Combinatorial Optimization 9 (2005) 147–156] and solved in O(nU) time when the edge lengths are positive integers, where n is the number of nodes in the tree and U is the length upper bound of the path. We present an algorithm that runs in O(nlog2n) time for the generalized case when the edge lengths are positive real numbers, which indicates an improvement when U=Ω(log2n). The complexity is reduced to O(nlogn) when edge lengths are uniform. In addition, we study the generalized problems of finding a length-constrained maximum-sum or maximum-density subtree in a given tree or graph, providing algorithmic and complexity results

Mining topological structure in graphs through forest representations

We consider the problem of inferring simplified topological substructures—which we term backbones—in metric and non-metric graphs. Intuitively, these are subgraphs with ‘few’ nodes, multifurcations, and cycles, that model the topology of the original graph well. We present a multistep procedure for inferring these backbones. First, we encode local (geometric) information of each vertex in the original graph by means of the boundary coefficient (BC) to identify ‘core’ nodes in the graph. Next, we construct a forest representation of the graph, termed an f-pine, that connects every node of the graph to a local ‘core’ node. The final backbone is then inferred from the f-pine through CLOF (Constrained Leaves Optimal subForest), a novel graph optimization problem we introduce in this paper. On a theoretical level, we show that CLOF is NP-hard for general graphs. However, we prove that CLOF can be efficiently solved for forest graphs, a surprising fact given that CLOF induces a nontrivial monotone submodular set function maximization problem on tree graphs. This result is the basis of our method for mining backbones in graphs through forest representation. We qualitatively and quantitatively confirm the applicability, effectiveness, and scalability of our method for discovering backbones in a variety of graph-structured data, such as social networks, earthquake locations scattered across the Earth, and high-dimensional cell trajectory dat

Hide-and-seek and other search games

In the game of hide-and-seek played between two players, a Hider picks a hiding place and a Searcher tries to find him in the least possible time. Since Isaacs had the idea of formulating this mathematically as a zero-sum game almost fifty years ago in his book, Differential Games, the theory of search games has been studied and developed extensively. In the classic model of search games on networks, first formalised by Gal in 1979, a Hider strategy is a point on the network and a Searcher strategy is a constant speed path starting from a designated point of the network. The Searcher wishes to minimise the time to find the Hider (the payoff), and the Hider wishes to maximise it. Gal solved this game for certain classes of networks: that is, he found optimal strategies and the payoff assuming best play on both sides. Here we study new formulations of search games, starting with a model proposed by Alpern where the speed of the Searcher depends on which direction he is traveling. We give a solution of this game on a class of networks called trees, generalising Gal's work. We also show how the game relates to another new model of search studied by Baston and Kikuta, where the Searcher must pay extra search costs to search the network's nodes (or vertices). We go on to study another new model of search called expanding search, which models coal mining. We solve this game on trees and also study the related problem where the Hider's strategy is known to the Searcher. We extend the expanding search game to consider what happens if there are several hidden objects and solve this game for certain classes of networks. Finally we study a game in which a squirrel hides nuts from a pilferer

Performance optimization of wireless sensor networks for remote monitoring

Wireless sensor networks (WSNs) have gained worldwide attention in recent years because of their great potential for a variety of applications such as hazardous environment exploration, military surveillance, habitat monitoring, seismic sensing, and so on. In this thesis we study the use of WSNs for remote monitoring, where a wireless sensor network is deployed in a remote region for sensing phenomena of interest while its data monitoring center is located in a metropolitan area that is geographically distant from the monitored region. This application scenario poses great challenges since such kind of monitoring is typically large scale and expected to be operational for a prolonged period without human involvement. Also, the long distance between the monitored region and the data monitoring center requires that the sensed data must be transferred by the employment of a third-party communication service, which incurs service costs. Existing methodologies for performance optimization of WSNs base on that both the sensor network and its data monitoring center are co-located, and therefore are no longer applicable to the remote monitoring scenario. Thus, developing new techniques and approaches for severely resource-constrained WSNs is desperately needed to maintain sustainable, unattended remote monitoring with low cost. Specifically, this thesis addresses the key issues and tackles problems in the deployment of WSNs for remote monitoring from the following aspects. To maximize the lifetime of large-scale monitoring, we deal with the energy consumption imbalance issue by exploring multiple sinks. We develop scalable algorithms which determine the optimal number of sinks needed and their locations, thereby dynamically identifying the energy bottlenecks and balancing the data relay workload throughout the network. We conduct experiments and the experimental results demonstrate that the proposed algorithms significantly prolong the network lifetime. To eliminate imbalance of energy consumption among sensor nodes, a complementary strategy is to introduce a mobile sink for data gathering. However, the limited communication time between the mobile sink and nodes results in that only part of sensed data will be collected and the rest will be lost, for which we propose the concept of monitoring quality with the exploration of sensed data correlation among nodes. We devise a heuristic for monitoring quality maximization, which schedules the sink to collect data from selected nodes, and uses the collected data to recover the missing ones. We study the performance of the proposed heuristic and validate its effectiveness in improving the monitoring quality. To strive for the fine trade-off between two performance metrics: throughput and cost, we investigate novel problems of minimizing cost with guaranteed throughput, and maximizing throughput with minimal cost. We develop approximation algorithms which find reliable data routing in the WSN and strategically balance workload on the sinks. We prove that the delivered solutions are fractional of the optimum. We finally conclude our work and discuss potential research topics which derive from the studies of this thesis

The bi-objective travelling salesman problem with profits and its connection to computer networks.

This is an interdisciplinary work in Computer Science and Operational Research. As it is well known, these two very important research fields are strictly connected. Among other aspects, one of the main areas where this interplay is strongly evident is Networking. As far as most recent decades have seen a constant growing of every kind of network computer connections, the need for advanced algorithms that help in optimizing the network performances became extremely relevant. Classical Optimization-based approaches have been deeply studied and applied since long time. However, the technology evolution asks for more flexible and advanced algorithmic approaches to model increasingly complex network configurations. In this thesis we study an extension of the well known Traveling Salesman Problem (TSP): the Traveling Salesman Problem with Profits (TSPP). In this generalization, a profit is associated with each vertex and it is not necessary to visit all vertices. The goal is to determine a route through a subset of nodes that simultaneously minimizes the travel cost and maximizes the collected profit. The TSPP models the problem of sending a piece of information through a network where, in addition to the sending costs, it is also important to consider what “profit” this information can get during its routing. Because of its formulation, the right way to tackled the TSPP is by Multiobjective Optimization algorithms. Within this context, the aim of this work is to study new ways to solve the problem in both the exact and the approximated settings, giving all feasible instruments that can help to solve it, and to provide experimental insights into feasible networking instances