Optimal Acyclic Hamiltonian Path Completion for Outerplanar Triangulated st-Digraphs (with Application to Upward Topological Book Embeddings)

Given an embedded planar acyclic digraph G, we define the problem of "acyclic hamiltonian path completion with crossing minimization (Acyclic-HPCCM)" to be the problem of determining an hamiltonian path completion set of edges such that, when these edges are embedded on G, they create the smallest possible number of edge crossings and turn G to a hamiltonian digraph. Our results include: --We provide a characterization under which a triangulated st-digraph G is hamiltonian. --For an outerplanar triangulated st-digraph G, we define the st-polygon decomposition of G and, based on its properties, we develop a linear-time algorithm that solves the Acyclic-HPCCM problem with at most one crossing per edge of G. --For the class of st-planar digraphs, we establish an equivalence between the Acyclic-HPCCM problem and the problem of determining an upward 2-page topological book embedding with minimum number of spine crossings. We infer (based on this equivalence) for the class of outerplanar triangulated st-digraphs an upward topological 2-page book embedding with minimum number of spine crossings and at most one spine crossing per edge. To the best of our knowledge, it is the first time that edge-crossing minimization is studied in conjunction with the acyclic hamiltonian completion problem and the first time that an optimal algorithm with respect to spine crossing minimization is presented for upward topological book embeddings

Occupational Fraud Detection Through Visualization

Occupational fraud affects many companies worldwide causing them economic loss and liability issues towards their customers and other involved entities. Detecting internal fraud in a company requires significant effort and, unfortunately cannot be entirely prevented. The internal auditors have to process a huge amount of data produced by diverse systems, which are in most cases in textual form, with little automated support. In this paper, we exploit the advantages of information visualization and present a system that aims to detect occupational fraud in systems which involve a pair of entities (e.g., an employee and a client) and periodic activity. The main visualization is based on a spiral system on which the events are drawn appropriately according to their time-stamp. Suspicious events are considered those which appear along the same radius or on close radii of the spiral. Before producing the visualization, the system ranks both involved entities according to the specifications of the internal auditor and generates a video file of the activity such that events with strong evidence of fraud appear first in the video. The system is also equipped with several different visualizations and mechanisms in order to meet the requirements of an internal fraud detection system

Optimal Algorithms for Multipacket Routing Problems on Rings

We study multipacket routing problems. We divide the multipacket routing problem into two classes, namely, distance limited and bisection limited routing problems. Then, we concentrate on rings of processors. We prove a new lower bound of 2n/ 3 routing steps for the case of distance limited routing problems. We also give an algorithm that tightens this lower bound. For bisection limited problems the lower bound is kn/ 4,k \u3e2, where k is the number of packets per processor. The trivial algorithm needs in the worst case k | n /2| steps to terminate. An algorithm that completes the routing in kn /4 + 2.5 n routing steps is given. We define the class of pure routing algorithms and we demonstrate that new lower bounds hold if the routing is to be done by an algorithm in this class

Multi-level caching with delayed-multicast for video-on-demand

Delayed-Multicast is a novel transmission technique to support Video-on-Demand. It introduces buffers within the network to bridge the temporal delays between similar requests thus minimizing the aggregate bandwidth and server load. This paper introduces an improved online algorithm for resource allocation with Delayed-Multicast by utilizing prior knowledge of each clip's popularity. The algorithm is intended to be simple so as to allow for deployment at multiple levels in a distribution network. The result is greater backbone traffic savings and a corresponding reduction in the server load

Many-to-One Boundary Labeling with Backbones

In this paper we study \emph{many-to-one boundary labeling with backbone leaders}. In this new many-to-one model, a horizontal backbone reaches out of each label into the feature-enclosing rectangle. Feature points that need to be connected to this label are linked via vertical line segments to the backbone. We present dynamic programming algorithms for label number and total leader length minimization of crossing-free backbone labelings. When crossings are allowed, we aim to obtain solutions with the minimum number of crossings. This can be achieved efficiently in the case of fixed label order, however, in the case of flexible label order we show that minimizing the number of leader crossings is NP-hard.Comment: 23 pages, 10 figures, this is the full version of a paper that is about to appear in GD'1