A Sidetrack-Based Algorithm for Finding the k Shortest Simple Paths in a Directed Graph

We present an algorithm for the k shortest simple path problem on weighted directed graphs (kSSP) that is based on Eppstein's algorithm for a similar problem in which paths are allowed to contain cycles. In contrast to most other algorithms for kSSP, ours is not based on Yen's algorithm and does not solve replacement path problems. Its worst-case running time is on par with state-of-the-art algorithms for kSSP. Using our algorithm, one may find O(m) simple paths with a single shortest path tree computation and O(n + m) additional time per path in well-behaved cases, where n is the number of nodes and m is the number of edges. Our computational results show that on random graphs and large road networks, these well-behaved cases are quite common and our algorithm is faster than existing algorithms by an order of magnitude. Further, the running time is far better predictable due to very small dispersion

Blazing a Trail via Matrix Multiplications: A Faster Algorithm for Non-Shortest Induced Paths

For vertices $u$ and $v$ of an $n$-vertex graph $G$, a $uv$-trail of $G$ is an induced $uv$-path of $G$ that is not a shortest $uv$-path of $G$. Berger, Seymour, and Spirkl [Discrete Mathematics 2021] gave the previously only known polynomial-time algorithm, running in $O(n^{18})$ time, to either output a $uv$-trail of $G$ or ensure that $G$ admits no $uv$-trail. We reduce the complexity to the time required to perform a poly-logarithmic number of multiplications of $n^2\times n^2$ Boolean matrices, leading to a largely improved $O(n^{4.75})$-time algorithm.Comment: 18 pages, 6 figures, a preliminary version appeared in STACS 202

Space and Time Trade-Off for the k Shortest Simple Paths Problem

The k shortest simple path problem (kSSP) asks to compute a set of top-k shortest simple paths from a vertex s to a vertex t in a digraph. Yen (1971) proposed the first algorithm with the best known theoretical complexity of O(kn(m+n log n)) for a digraph with n vertices and m arcs. Since then, the problem has been widely studied from an algorithm engineering perspective, and impressive improvements have been achieved. In particular, Kurz and Mutzel (2016) proposed a sidetracks-based (SB) algorithm which is currently the fastest solution. In this work, we propose two improvements of this algorithm. We first show how to speed up the SB algorithm using dynamic updates of shortest path trees. We did experiments on some road networks of the 9th DIMAC\u27S challenge with up to about half a million nodes and one million arcs. Our computational results show an average speed up by a factor of 1.5 to 2 with a similar working memory consumption as SB. We then propose a second algorithm enabling to significantly reduce the working memory at the cost of an increase of the running time (up to two times slower). Our experiments on the same data set show, on average, a reduction by a factor of 1.5 to 2 of the working memory

Finding Useful Detours in Geographical Databases

In geographical databases for navigation, users raise various types of queries concerning route guidance. The most fundamental query is a shortest-route query, but, as dynamical traffic information newly becomes available and the static geographical database of roads itself has grown up further, more flexible queries are required to realize a user-friendly interface meeting the current settings. One important query among them is a detour query which provides information about detours, say listing several candidates for useful detours. This paper first reviews algorithms for the shortest and k shortest paths, and discusses their extensions to detour queries. Algorithms for finding a realistic detour are given. The efficiency and property of the algorithms are examined through experiments on an actual road network.PAPE

Hybrid Evolutionary Routing Optimisation for Wireless Sensor Mesh Networks

Battery powered wireless sensors are widely used in industrial and regulatory monitoring applications. This is primarily due to the ease of installation and the ability to monitor areas that are difficult to access. Additionally, they can be left unattended for long periods of time. However, there are many challenges to successful deployments of wireless sensor networks (WSNs). In this thesis we draw attention to two major challenges. Firstly, with a view to extending network range, modern WSNs use mesh network topologies, where data is sent either directly or by relaying data from node-to-node en route to the central base station. The additional load of relaying other nodes’ data is expensive in terms of energy consumption, and depending on the routes taken some nodes may be heavily loaded. Hence, it is crucial to locate routes that achieve energy efficiency in the network and extend the time before the first node exhausts its battery, thus improving the network lifetime. Secondly, WSNs operate in a dynamic radio environment. With changing conditions, such as modified buildings or the passage of people, links may fail and data will be lost as a consequence. Therefore in addition to finding energy efficient routes, it is important to locate combinations of routes that are robust to the failure of radio links. Dealing with these challenges presents a routing optimisation problem with multiple objectives: find good routes to ensure energy efficiency, extend network lifetime and improve robustness. This is however an NP-hard problem, and thus polynomial time algorithms to solve this problem are unavailable. Therefore we propose hybrid evolutionary approaches to approximate the optimal trade-offs between these objectives. In our approach, we use novel search space pruning methods for network graphs, based on k-shortest paths, partially and edge disjoint paths, and graph reduction to combat the combinatorial explosion in search space size and consequently conduct rapid optimisation. The proposed methods can successfully approximate optimal Pareto fronts. The estimated fronts contain a wide range of robust and energy efficient routes. The fronts typically also include solutions with a network lifetime close to the optimal lifetime if the number of routes per nodes were unconstrained. These methods are demonstrated in a real network deployed at the Victoria & Albert Museum, London, UK.Part of this work was supported by a knowledge transfer partnership (KTP) awarded to the IMC Group Ltd. and the University of Exeter (KTP008748).University of Exeter has provided financial support for the student

An Alternative Fuel Refueling Station Location Model considering Detour Traffic Flows on a Highway Road System

With the development of alternative fuel (AF) vehicle technologies, studies on finding the potential location of AF refueling stations in transportation networks have received considerable attention. Due to the strong limited driving range, AF vehicles for long-distance intercity trips may require multiple refueling stops at different locations on the way to their destination, which makes the AF refueling station location problem more challenging. In this paper, we consider that AF vehicles requiring multiple refueling stops at different locations during their long-distance intercity trips are capable of making detours from their preplanned paths and selecting return paths that may be different from original paths for their round trips whenever AF refueling stations are not available along the preplanned paths. These options mostly need to be considered when an AF refueling infrastructure is not fully developed on a highway system. To this end, we first propose an algorithm to generate alternative paths that may provide the multiple AF refueling stops between all origin/destination (OD) vertices. Then, a new mixed-integer programming model is proposed to locate AF refueling stations within a preselected set of candidate sites on a directed transportation network by maximizing the coverage of traffic flows along multiple paths. We first test our mathematical model with the proposed algorithm on a classical 25-vertex network with 25 candidate sites through various scenarios that consider a different number of paths for each OD pair, deviation factors, and limited driving ranges of vehicles. Then, we apply our proposed model to locate liquefied natural gas refueling stations in the state of Pennsylvania considering the construction budget. Our results show that the number of alternative paths and deviation distance available significantly affect the coverage of traffic flows at the stations as well as computational time

Optimal Path Queries in Very Large Spatial Databases

Researchers have been investigating the optimal route query problem for a long time. Optimal route queries are categorized as either unconstrained or constrained queries. Many main memory based algorithms have been developed to deal with the optimal route query problem. Among these, Dijkstra's shortest path algorithm is one of the most popular algorithms for the unconstrained route query problem. The constrained route query problem is more complicated than the unconstrained one, and some constrained route query problems such as the Traveling Salesman Problem and Hamiltonian Path Problem are NP-hard. There are many algorithms dealing with the constrained route query problem, but most of them only solve a specific case. In addition, all of them require that the entire graph resides in the main memory. Recently, due to the need of applications in very large graphs, such as the digital maps managed by Geographic Information Systems (GIS), several disk-based algorithms have been derived by using divide-and-conquer techniques to solve the shortest path problem in a very large graph. However, until now little research has been conducted on the disk-based constrained problem. This thesis presents two algorithms: 1) a new disk-based shortest path algorithm (DiskSPNN), and 2) a new disk-based optimal path algorithm (DiskOP) that answers an optimal route query without passing a set of forbidden edges in a very large graph. Both algorithms fit within the same divide-and-conquer framework as the existing disk-based shortest path algorithms proposed by Ning Zhang and Heechul Lim. Several techniques, including query super graph, successor fragment and open boundary node pruning are proposed to improve the performance of the previous disk-based shortest path algorithms. Furthermore, these techniques are applied to the DiskOP algorithm with minor changes. The proposed DiskOP algorithm depends on the concept of collecting a set of boundary vertices and simultaneously relaxing their adjacent super edges. Even if the forbidden edges are distributed in all the fragments of a graph, the DiskOP algorithm requires little memory. Our experimental results indicate that the DiskSPNN algorithm performs better than the original ones with respect to the I/O cost as well as the running time, and the DiskOP algorithm successfully solves a specific constrained route query problem in a very large graph

Interpretable methods in cancer diagnostics

Cancer is a hard problem. It is hard for the patients, for the doctors and nurses, and for the researchers working on understanding the disease and finding better treatments for it. The challenges faced by a pathologist diagnosing the disease for a patient is not necessarily the same as the ones faced by cell biologists working on experimental treatments and understanding the fundamentals of cancer. In this thesis we work on different challenges faced by both of the above teams. This thesis first presents methods to improve the analysis of the flow cy- tometry data used frequently in the diagnosis process, specifically for the two subtypes of non-Hodgkin Lymphoma which are our focus: Follicular Lymphoma and Diffuse Large B Cell Lymphoma. With a combination of concepts from graph theory, dynamic programming, and machine learning, we present methods to improve the diagnosis process and the analysis of the abovementioned data. The interpretability of the method helps a pathologist to better understand a patient’s disease, which itself improves their choices for a treatment. In the second part, we focus on the analysis of DNA-methylation and gene expression data, both of which presenting the challenge of being very high dimen- sional yet with a few number of samples comparatively. We present an ensemble model which adapts to different patterns seen in each given data, in order to adapt to noise and batch effects. At the same time, the interpretability of our model helps a pathologist to better find and tune the treatment for the patient: a step further towards personalized medicine.Krebs ist ein schweres Problem. Es ist schwer für die Patienten, für die Ärzte und Krankenschwestern und für die Forscher, die daran arbeiten, die Krankheit zu verstehen und eine bessere Behandlung dafür zu finden. Die Herausforderungen, mit denen ein Pathologe konfrontiert ist, um die Krankheit eines Patienten zu diagnostizieren, müssen nicht die gleichen sein, mit denen Zellbiologen konfrontiert sind, die an experimentellen Behandlungen arbeiten und die Grundlagen von Krebs verstehen. In dieser Arbeit beschäftigen wir uns mit verschiedenen Herausforderungen, denen sich beide oben genannten Teams stellen. In dieser Arbeit werden zunächst Methoden vorgestellt, um die Analyse der im Diagnoseverfahren häufig verwendeten Durchflusszytometriedaten zu verbessern, insbesondere für die beiden Subtypen des Non-Hodgkin-Lymphoms, auf die wir uns konzentrieren: das follikuläre Lymphom und das diffuse großzellige B-Zell-Lymphom. Mit einer Kombination von Konzepten aus Graphentheorie, dynamischer Programmierung und künstliche Intelligenz präsentieren wir Methoden zur Verbesserung des Diagnoseprozesses und der Analyse der oben genannten Daten. Die Interpretierbarkeit der Methode hilft einem Pathologen, die Apatientenkrankheit besser zu verstehen, was wiederum seine Wahlmöglichkeiten für eine Behandlung verbessert. Im zweiten Teil konzentrieren wir uns auf die Analyse von DNA-Methylierungsund Genexpressionsdaten, die beide die Herausforderung darstellen, sehr hochdimensional zu sein, jedoch mit nur wenigen Proben im Vergleich.Wir präsentieren ein Zusammenstellungsmodell, das sich an unterschiedliche Muster anpasst, die in den jeweiligen Daten zu sehen sind, um sich an Rauschen und Batch-Effekte anzupassen. Gleichzeitig hilft die Interpretierbarkeit unseres Modells einem Pathologen, die Behandlung für den Patienten besser zu finden und abzustimmen: ein Schritt weiter in Richtung personalisierter Medizin