Rerouting shortest paths in planar graphs

A rerouting sequence is a sequence of shortest st-paths such that consecutive paths differ in one vertex. We study the the Shortest Path Rerouting Problem, which asks, given two shortest st-paths P and Q in a graph G, whether a rerouting sequence exists from P to Q. This problem is PSPACE-hard in general, but we show that it can be solved in polynomial time if G is planar. To this end, we introduce a dynamic programming method for reconfiguration problems.Comment: submitte

The Complexity of Rerouting Shortest Paths

The Shortest Path Reconfiguration problem has as input a graph G (with unit edge lengths) with vertices s and t, and two shortest st-paths P and Q. The question is whether there exists a sequence of shortest st-paths that starts with P and ends with Q, such that subsequent paths differ in only one vertex. This is called a rerouting sequence. This problem is shown to be PSPACE-complete. For claw-free graphs and chordal graphs, it is shown that the problem can be solved in polynomial time, and that shortest rerouting sequences have linear length. For these classes, it is also shown that deciding whether a rerouting sequence exists between all pairs of shortest st-paths can be done in polynomial time. Finally, a polynomial time algorithm for counting the number of isolated paths is given.Comment: The results on claw-free graphs, chordal graphs and isolated paths have been added in version 2 (april 2012). Version 1 (September 2010) only contained the PSPACE-hardness result. (Version 2 has been submitted.

REROUTING JALUR PIPA AVTUR PADA PROYEK PEMBANGUNAN DEPOT PENGISIAN PESAWAT UDARA DI KULON PROGO

Abstract – The construction phase of the Airplane Refueling Station project has begun, but a constructionerror occurred, resulting in the crash of line number 31-6"-JA-A-511 with the platform and causingdisplacement due to thermal expansion loads. Based on this issue, two alternative rerouting options wereproposed: alternative rerouting 1 and alternative rerouting 2. The calculation of the allowable pipe span forboth designs resulted in a value of 7.27 ft with 9 supports, using rest guides and u-bolts as support types. Theflexibility values for both new designs were found to be below K1, meeting the criteria. The largest sustainedload stress was calculated to be 4019 psi, the largest occasional load stress was 4211 psi, and the largestthermal expansion load stress was 5404 psi. These stress values were obtained from alternative rerouting 1,indicating that alternative rerouting 1 has higher stress values compared to alternative rerouting 2. Stresscalculations for both alternative rerouting 1 and alternative rerouting 2 were performed using stress analysissoftware. The cost analysis results for alternative rerouting 1 amounted to Rp 50,364,623, while the costanalysis for alternative rerouting 2 amounted to Rp 49,080,623. Therefore, based on the comparison of stressanalysis and cost analysis, alternative rerouting 2 is chosen as it has lower stress values and more affordablecosts

Error and Attack Tolerance of Layered Complex Networks

Many complex systems may be described not by one, but by a number of complex networks mapped one on the other in a multilayer structure. The interactions and dependencies between these layers cause that what is true for a distinct single layer does not necessarily reflect well the state of the entire system. In this paper we study the robustness of three real-life examples of two-layer complex systems that come from the fields of communication (the Internet), transportation (the European railway system) and biology (the human brain). In order to cover the whole range of features specific to these systems, we focus on two extreme policies of system's response to failures, no rerouting and full rerouting. Our main finding is that multilayer systems are much more vulnerable to errors and intentional attacks than they seem to be from a single layer perspective.Comment: 5 pages, 3 figure

Logical topology design for IP rerouting: ASONs versus static OTNs

IP-based backbone networks are gradually moving to a network model consisting of high-speed routers that are flexibly interconnected by a mesh of light paths set up by an optical transport network that consists of wavelength division multiplexing (WDM) links and optical cross-connects. In such a model, the generalized MPLS protocol suite could provide the IP centric control plane component that will be used to deliver rapid and dynamic circuit provisioning of end-to-end optical light paths between the routers. This is called an automatic switched optical (transport) network (ASON). An ASON enables reconfiguration of the logical IP topology by setting up and tearing down light paths. This allows to up- or downgrade link capacities during a router failure to the capacities needed by the new routing of the affected traffic. Such survivability against (single) IP router failures is cost-effective, as capacity to the IP layer can be provided flexibly when necessary. We present and investigate a logical topology optimization problem that minimizes the total amount or cost of the needed resources (interfaces, wavelengths, WDM line-systems, amplifiers, etc.) in both the IP and the optical layer. A novel optimization aspect in this problem is the possibility, as a result of the ASON, to reuse the physical resources (like interface cards and WDM line-systems) over the different network states (the failure-free and all the router failure scenarios). We devised a simple optimization strategy to investigate the cost of the ASON approach and compare it with other schemes that survive single router failures

Multi-agent pathfinding for unmanned aerial vehicles

Unmanned aerial vehicles (UAVs), commonly known as drones, have become more and more prevalent in recent years. In particular, governmental organizations and companies around the world are starting to research how UAVs can be used to perform tasks such as package deliver, disaster investigation and surveillance of key assets such as pipelines, railroads and bridges. NASA is currently in the early stages of developing an air traffic control system specifically designed to manage UAV operations in low-altitude airspace. Companies such as Amazon and Rakuten are testing large-scale drone deliver services in the USA and Japan. To perform these tasks, safe and conflict-free routes for concurrently operating UAVs must be found. This can be done using multi-agent pathfinding (mapf) algorithms, although the correct choice of algorithms is not clear. This is because many state of the art mapf algorithms have only been tested in 2D space in maps with many obstacles, while UAVs operate in 3D space in open maps with few obstacles. In addition, when an unexpected event occurs in the airspace and UAVs are forced to deviate from their original routes while inflight, new conflict-free routes must be found. Planning for these unexpected events is commonly known as contingency planning. With manned aircraft, contingency plans can be created in advance or on a case-by-case basis while inflight. The scale at which UAVs operate, combined with the fact that unexpected events may occur anywhere at any time make both advanced planning and planning on a case-by-case basis impossible. Thus, a new approach is needed. Online multi-agent pathfinding (online mapf) looks to be a promising solution. Online mapf utilizes traditional mapf algorithms to perform path planning in real-time. That is, new routes for UAVs are found while inflight. The primary contribution of this thesis is to present one possible approach to UAV contingency planning using online multi-agent pathfinding algorithms, which can be used as a baseline for future research and development. It also provides an in-depth overview and analysis of offline mapf algorithms with the goal of determining which ones are likely to perform best when applied to UAVs. Finally, to further this same goal, a few different mapf algorithms are experimentally tested and analyzed

Cyclically five-connected cubic graphs

A cubic graph $G$ is cyclically 5-connected if $G$ is simple, 3-connected, has at least 10 vertices and for every set $F$ of edges of size at most four, at most one component of $G\backslash F$ contains circuits. We prove that if $G$ and $H$ are cyclically 5-connected cubic graphs and $H$ topologically contains $G$, then either $G$ and $H$ are isomorphic, or (modulo well-described exceptions) there exists a cyclically 5-connected cubic graph $G'$ such that $H$ topologically contains $G'$ and $G'$ is obtained from $G$ in one of the following two ways. Either $G'$ is obtained from $G$ by subdividing two distinct edges of $G$ and joining the two new vertices by an edge, or $G'$ is obtained from $G$ by subdividing each edge of a circuit of length five and joining the new vertices by a matching to a new circuit of length five disjoint from $G$ in such a way that the cyclic orders of the two circuits agree. We prove a companion result, where by slightly increasing the connectivity of $H$ we are able to eliminate the second construction. We also prove versions of both of these results when $G$ is almost cyclically 5-connected in the sense that it satisfies the definition except for 4-edge cuts such that one side is a circuit of length four. In this case $G'$ is required to be almost cyclically 5-connected and to have fewer circuits of length four than $G$. In particular, if $G$ has at most one circuit of length four, then $G'$ is required to be cyclically 5-connected. However, in this more general setting the operations describing the possible graphs $G'$ are more complicated.Comment: 47 pages, 5 figures. Revised according to referee's comments. To appear in J. Combin. Theory Ser.