From BGP to RTT and Beyond: Matching BGP Routing Changes and Network Delay Variations with an Eye on Traceroute Paths

Many organizations have the mission of assessing the quality of broadband access services offered by Internet Service Providers (ISPs). They deploy network probes that periodically perform network measures towards selected Internet services. By analyzing the data collected by the probes it is often possible to gain a reasonable estimate of the bandwidth made available by the ISP. However, it is much more difficult to use such data to explain who is responsible of the fluctuations of other network qualities. This is especially true for latency, that is fundamental for several nowadays network services. On the other hand, there are many publicly accessible BGP routers that collect the history of routing changes and that are good candidates to be used for understanding if latency fluctuations depend on interdomain routing. In this paper we provide a methodology that, given a probe that is located inside the network of an ISP and that executes latency measures and given a set of publicly accessible BGP routers located inside the same ISP, decides which routers are best candidates (if any) for studying the relationship between variations of network performance recorded by the probe and interdomain routing changes. We validate the methodology with experimental studies based on data gathered by the RIPE NCC, an organization that is well-known to be independent and that publishes both BGP data within the Routing Information Service (RIS) and probe measurement data within the Atlas project

Intra-Domain Pathlet Routing

Internal routing inside an ISP network is the foundation for lots of services that generate revenue from the ISP's customers. A fine-grained control of paths taken by network traffic once it enters the ISP's network is therefore a crucial means to achieve a top-quality offer and, equally important, to enforce SLAs. Many widespread network technologies and approaches (most notably, MPLS) offer limited (e.g., with RSVP-TE), tricky (e.g., with OSPF metrics), or no control on internal routing paths. On the other hand, recent advances in the research community are a good starting point to address this shortcoming, but miss elements that would enable their applicability in an ISP's network. We extend pathlet routing by introducing a new control plane for internal routing that has the following qualities: it is designed to operate in the internal network of an ISP; it enables fine-grained management of network paths with suitable configuration primitives; it is scalable because routing changes are only propagated to the network portion that is affected by the changes; it supports independent configuration of specific network portions without the need to know the configuration of the whole network; it is robust thanks to the adoption of multipath routing; it supports the enforcement of QoS levels; it is independent of the specific data plane used in the ISP's network; it can be incrementally deployed and it can nicely coexist with other control planes. Besides formally introducing the algorithms and messages of our control plane, we propose an experimental validation in the simulation framework OMNeT++ that we use to assess the effectiveness and scalability of our approach.Comment: 13 figures, 1 tabl

Strip Planarity Testing of Embedded Planar Graphs

In this paper we introduce and study the strip planarity testing problem, which takes as an input a planar graph $G(V,E)$ and a function $\gamma:V \rightarrow \{1,2,\dots,k\}$ and asks whether a planar drawing of $G$ exists such that each edge is monotone in the $y$-direction and, for any $u,v\in V$ with $\gamma(u)<\gamma(v)$, it holds $y(u)<y(v)$. The problem has strong relationships with some of the most deeply studied variants of the planarity testing problem, such as clustered planarity, upward planarity, and level planarity. We show that the problem is polynomial-time solvable if $G$ has a fixed planar embedding.Comment: 24 pages, 12 figures, extended version of 'Strip Planarity Testing' (21st International Symposium on Graph Drawing, 2013

Ptolomaeus: the Web Cartographer

The hugeness of the Web and its continuous growth have made navigation in the Internet extremely difficult. The new advanced features provided by HTML extensions and scripting languages allow a common browser to manage powerful hypermedial representation in each single page but leave unsolved some structural problems of the Web. In fact, the process of finding information by surfing the Web is mainly hindered by the lack of a reasonable schema in the hyperspace; broken and redundant links make the problem even worse. This leads the user to become ”lost in the hyperspace” (LH-Syndrome)

A Tipping Point for the Planarity of Small and Medium Sized Graphs

This paper presents an empirical study of the relationship between the density of small-medium sized random graphs and their planarity. It is well known that, when the number of vertices tends to infinite, there is a sharp transition between planarity and non-planarity for edge density d=0.5. However, this asymptotic property does not clarify what happens for graphs of reduced size. We show that an unexpectedly sharp transition is also exhibited by small and medium sized graphs. Also, we show that the same "tipping point" behavior can be observed for some restrictions or relaxations of planarity (we considered outerplanarity and near-planarity, respectively).Comment: Appears in the Proceedings of the 28th International Symposium on Graph Drawing and Network Visualization (GD 2020

Incremental Convex Planarity Testing

AbstractAn important class of planar straight-line drawings of graphs are convex drawings, in which all the faces are drawn as convex polygons. A planar graph is said to be convex planar if it admits a convex drawing. We give a new combinatorial characterization of convex planar graphs based on the decomposition of a biconnected graph into its triconnected components. We then consider the problem of testing convex planarity in an incremental environment, where a biconnected planar graph is subject to on-line insertions of vertices and edges. We present a data structure for the on-line incremental convex planarity testing problem with the following performance, where n denotes the current number of vertices of the graph: (strictly) convex planarity testing takes O(1) worst-case time, insertion of vertices takes O(log n) worst-case time, insertion of edges takes O(log n) amortized time, and the space requirement of the data structure is O(n)

Relaxing the Constraints of Clustered Planarity

In a drawing of a clustered graph vertices and edges are drawn as points and curves, respectively, while clusters are represented by simple closed regions. A drawing of a clustered graph is c-planar if it has no edge-edge, edge-region, or region-region crossings. Determining the complexity of testing whether a clustered graph admits a c-planar drawing is a long-standing open problem in the Graph Drawing research area. An obvious necessary condition for c-planarity is the planarity of the graph underlying the clustered graph. However, such a condition is not sufficient and the consequences on the problem due to the requirement of not having edge-region and region-region crossings are not yet fully understood. In order to shed light on the c-planarity problem, we consider a relaxed version of it, where some kinds of crossings (either edge-edge, edge-region, or region-region) are allowed even if the underlying graph is planar. We investigate the relationships among the minimum number of edge-edge, edge-region, and region-region crossings for drawings of the same clustered graph. Also, we consider drawings in which only crossings of one kind are admitted. In this setting, we prove that drawings with only edge-edge or with only edge-region crossings always exist, while drawings with only region-region crossings may not. Further, we provide upper and lower bounds for the number of such crossings. Finally, we give a polynomial-time algorithm to test whether a drawing with only region-region crossings exist for biconnected graphs, hence identifying a first non-trivial necessary condition for c-planarity that can be tested in polynomial time for a noticeable class of graphs