The energy-constrained quickest path problem

This paper addresses a variant of the quickest path problem in which each arc has an additional parameter associated to it representing the energy consumed during the transmission along the arc while each node is endowed with a limited power to transmit messages. The aim of the energy-constrained quickest path problem is to obtain a quickest path whose nodes are able to support the transmission of a message of a known size. After introducing the problem and proving the main theoretical results, a polynomial algorithm is proposed to solve the problem based on computing shortest paths in a sequence of subnetworks of the original network. In the second part of the paper, the bi-objective variant of this problem is considered in which the objectives are the transmission time and the total energy used. An exact algorithm is proposed to find a complete set of efficient paths. The computational experiments carried out show the performance of both algorithms

Arc Routing with Time-Dependent Travel Times and Paths

Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the speed functions on the complete graph. We argue that this model is often inadequate, in particular for arc routing problems involving services on edges of a road network. To fill this gap, we formally define the time-dependent capacitated arc routing problem (TDCARP), with travel and service speed functions given directly at the network level. Under these assumptions, the quickest path between locations can change over time, leading to a complex problem that challenges the capabilities of current solution methods. We introduce effective algorithms for preprocessing quickest paths in a closed form, efficient data structures for travel time queries during routing optimization, as well as heuristic and exact solution approaches for the TDCARP. Our heuristic uses the hybrid genetic search principle with tailored solution-decoding algorithms and lower bounds for filtering moves. Our branch-and-price algorithm exploits dedicated pricing routines, heuristic dominance rules and completion bounds to find optimal solutions for problem counting up to 75 services. Based on these algorithms, we measure the benefits of time-dependent routing optimization for different levels of travel-speed data accuracy

Second best toll and capacity optimisation in network: solution algorithm and policy implications

This paper looks at the first and second-best jointly optimal toll and road capacity investment problems from both policy and technical oriented perspectives. On the technical side, the paper investigates the applicability of the constraint cutting algorithm for solving the second-best problem under elastic demand which is formulated as a bilevel programming problem. The approach is shown to perform well despite several problems encountered by our previous work in Shepherd and Sumalee (2004). The paper then applies the algorithm to a small sized network to investigate the policy implications of the first and second-best cases. This policy analysis demonstrates that the joint first best structure is to invest in the most direct routes while reducing capacities elsewhere. Whilst unrealistic this acts as a useful benchmark. The results also show that certain second best policies can achieve a high proportion of the first best benefits while in general generating a revenue surplus. We also show that unless costs of capacity are known to be low then second best tolls will be affected and so should be analysed in conjunction with investments in the network

Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms

Complex networks vulnerability to module-based attacks

In the multidisciplinary field of Network Science, optimization of procedures for efficiently breaking complex networks is attracting much attention from practical points of view. In this contribution we present a module-based method to efficiently break complex networks. The procedure first identifies the communities in which the network can be represented, then it deletes the nodes (edges) that connect different modules by its order in the betweenness centrality ranking list. We illustrate the method by applying it to various well known examples of social, infrastructure, and biological networks. We show that the proposed method always outperforms vertex (edge) attacks which are based on the ranking of node (edge) degree or centrality, with a huge gain in efficiency for some examples. Remarkably, for the US power grid, the present method breaks the original network of 4941 nodes to many fragments smaller than 197 nodes (4% of the original size) by removing mere 164 nodes (~3%) identified by the procedure. By comparison, any degree or centrality based procedure, deleting the same amount of nodes, removes only 22% of the original network, i.e. more than 3800 nodes continue to be connected after thatComment: 8 pages, 8 figure

Modeling the complex dynamics of enzyme-pathway coevolution.

Peer reviewedPostprin

Social network support for data delivery infrastructures

Network infrastructures often need to stage content so that it is accessible to consumers. The standard solution, deploying the content on a centralised server, can be inadequate in several situations. Our thesis is that information encoded in social networks can be used to tailor content staging decisions to the user base and thereby build better data delivery infrastructures. This claim is supported by two case studies, which apply social information in challenging situations where traditional content staging is infeasible. Our approach works by examining empirical traces to identify relevant social properties, and then exploits them. The first study looks at cost-effectively serving the ``Long Tail'' of rich-media user-generated content, which need to be staged close to viewers to control latency and jitter. Our traces show that a preference for the unpopular tail items often spreads virally and is localised to some part of the social network. Exploiting this, we propose Buzztraq, which decreases replication costs by selectively copying items to locations favoured by viral spread. We also design SpinThrift, which separates popular and unpopular content based on the relative proportion of viral accesses, and opportunistically spins down disks containing unpopular content, thereby saving energy. The second study examines whether human face-to-face contacts can efficiently create paths over time between arbitrary users. Here, content is staged by spreading it through intermediate users until the destination is reached. Flooding every node minimises delivery times but is not scalable. We show that the human contact network is resilient to individual path failures, and for unicast paths, can efficiently approximate flooding in delivery time distribution simply by randomly sampling a handful of paths found by it. Multicast by contained flooding within a community is also efficient. However, connectivity relies on rare contacts and frequent contacts are often not useful for data delivery. Also, periods of similar duration could achieve different levels of connectivity; we devise a test to identify good periods. We finish by discussing how these properties influence routing algorithms.This work was supported by a St. John's College Benefactor's Scholarship and a Research Studentship from the Cambridge Philosophical Society