Valentino Di Donato

Bitconeview: visualization of flows in the bitcoin transaction graph

Bitcoin is a digital currency whose transactions are stored into a public ledger, called blockchain, that can be viewed as a directed graph with more than 70 million nodes, where each node represents a transaction and each edge represents Bitcoins flowing from one transaction to another one. We describe a system for the visual analysis of how and when a flow of Bitcoins mixes with other flows in the transaction graph. Such a system relies on high-level metaphors for the representation of the graph and the size and characteristics of transactions, allowing for high level analysis of big portions of it.

L-Drawings of Directed Graphs

We introduce L-drawings, a novel paradigm for representing directed graphs aiming at combining the readability features of orthogonal drawings with the expressive power of matrix representations. In an L-drawing, vertices have exclusive x- and y-coordinates and edges consist of two segments, one exiting the source vertically and one entering the destination horizontally. We study the problem of computing L-drawings using minimum ink. We prove its NP-completeness and provide a heuristic based on a polynomial-time algorithm that adds a vertex to a drawing using the minimum additional ink. We performed an experimental analysis of the heuristic which confirms its effectiveness.

Discovering high-impact routing events using traceroutes

With the increasing diffusion of Internet probing technologies, a large amount of regularly collected traceroutes are available for Internet Service Providers (ISPs) at low cost. We introduce a practically applicable methodology and algorithm that, given solely an arbitrary set of traceroutes, spot routing paths that change similarly over time, aggregate them into inferred events, and report each event along with the impacted observation points and a small set of IP addresses that can help identify its cause. The formal model at the basis of our methodology revolves around the notion of empathy, a relation that binds similarly behaving traceroutes. The correctness and completeness of our approach are based on structural properties that are easily expressed in terms of empathic measurements. We perform experiments with data from public measurement infrastructures like RIPE Atlas, showing the effectiveness of our algorithm in distilling events from a large amount of traceroute data. We also validate the accuracy of the inferred events against ground-truth knowledge of routing changes originating from induced and spontaneous routing events. Given these promising results, we believe our methodology can be an effective aid for ISPs to detect and track routing changes affecting many users (with potentially adverse effects on their connection quality).

RoutingWatch: Visual exploration and analysis of routing events

Network operators invest significant resources in monitoring and troubleshooting the infrastructure they run. Currently, the availability of large networks of probing devices, like, for example, RIPE Atlas, dramatically increases the amount of data an operator can rely on. In particular, the large amount of traceroutes they can produce are both an opportunity and a challenge. In this paper we provide a detailed description of RoutingWatch, a visual tool for interactively performing searches and analysis of routing events inferred from a large set of traceroutes. The key design choices of RoutingWatch are based on discussions with network operators. We evaluate the effectiveness of our approach by conducting a preliminary user study.

Exploring Flow Metrics in Dense Geographical Networks.

We present FLOWMATRIX, a system for the interactive exploration of time-labeled multivariate flows between pairs of geographic locations. FLOWMATRIX offers a coordinated visualization based on the interplay between a geographic map and a matrix that allow to discover trends tied to specific locations while offering an overview of metrics of the flows between all pairs of locations. The input data is clustered following a geographic hierarchy and the user can navigate between different levels of detail. The design of our system privileges the execution of simple tasks like assessing the volume and features of the flows between pairs of locations, enumerating destinations with poor performance, and sorting flow streams based on their volume.

Windrose Planarity: Embedding Graphs with Direction-Constrained Edges

Given a planar graph G and a partition of the neighbors of each vertex v in four sets v↗, v↖, v↙, and v↘, the problem Windrose Planarity asks to decide whether G admits a windrose-planar drawing, that is, a planar drawing in which (i) each neighbor u ∈ v↗v is above and to the right of v, (ii) each neighbor u ∈ v↖ is above and to the left of v, (iii) each neighbor u ∈ v↙ is below and to the left of v, (iv) each neighbor u ∈ v↘ is below and to the right of v, and (v) edges are represented by curves that are monotone with respect to each axis. By exploiting both the horizontal and the vertical relationship among vertices, windrose-planar drawings allow us to simultaneously visualize two partial orders defined by means of the edges of the graph. Although the problem is NP-hard in the general case, we give a polynomial-time algorithm for testing whether there exists a windrose-planar drawing that respects a given combinatorial embedding. This algorithm is based on a characterization of the plane triangulations admitting a windrose-planar drawing. Furthermore, for any embedded graph with n vertices that has a windrose-planar drawing, we can construct one with at most one bend per edge and with at most 2n−5 bends in total, which lies on the 3n × 3n grid. The latter result contrasts with the fact that straight-line windrose-planar drawings may require exponential area.

Visualizing Co-phylogenetic Reconciliations

We introduce a hybrid metaphor for the visualization of the reconciliations of co-phylogenetic trees, that are mappings among the nodes of two trees. The typical application is the visualization of the co-evolution of hosts and parasites in biology. Our strategy combines a space-filling and a node-link approach. Differently from traditional methods, it guarantees an unambiguous and ‘downward’ representation whenever the reconciliation is time-consistent (i.e., meaningful). We address the problem of the minimization of the number of crossings in the representation, by giving a characterization of planar instances and by establishing the complexity of the problem. Finally, we propose heuristics for computing representations with few crossings.

Long Transaction Chains and the Bitcoin Heartbeat

Over the past few years a persistent growth of the number of daily Bitcoin transactions has been observed. This trend however, is known to be influenced by a number of phenomena that generate long transaction chains that are not related to real purchases (e.g. wallets shuffling and coin mixing). For a transaction chain we call transaction chain frequency the number of transactions of the chain divided by the time interval of the chain. In this paper, we first analyze to which extent Bitcoin transactions are involved in high frequency transaction chains, in the short and in the long term. Based on this analysis, we then argue that a large fraction of transactions do not refer to explicit human activity, namely to transactions between users that trade goods or services. Finally, we show that most of the transactions are involved into chains whose frequency is roughly stable over time and that we call Bitcoin Heartbeat.