We propose an algorithm for the problem of computing shortest paths among curved obstacles in the plane. If the obstacles have $O(n)$ description complexity, then the algorithm runs in $O(n\log n)$ time plus a term dependent on the properties of the boundary arcs. Specifically, if the arcs allow a certain kind of bisector intersection to be computed in constant time, or even in $O(\log n)$ time, then the running time of the overall algorithm is $O(n \log n)$. If the arcs support only constant-time tangent, intersection, and length queries, as is customarily assumed, then the algorithm computes an approximate shortest path, with relative error $\varepsilon$, in time $O(n\log n + n\log \frac{1}{\varepsilon})$. In fact, the algorithm computes an approximate shortest path map, a data structure with $O(n\log n)$ size, that allows it to report the (approximate) length of a shortest path from a fixed source point to any query point in the plane in $O(\log n)$ time. By applying an idea due to Wang [ Proceedings of the $32$nd Annual ACM-SIAM Symposium on Discrete Algorithms, 2021, pp. 810--821], the algorithm's working storage and the size of the approximate shortest path map can be reduced to $O(n)$.

Self-sovereign identity provides a feasible alternative to login via username and password through an identity provider to access digital services. It allows identity subjects to control and own their data. Although this is an appealing approach, it requires a whole new infrastructure with almost no dependencies on the existing ones. We designed and implemented a solution that combines an existing federated identity access management solution with the new approach by enabling authentication via self-sovereign-identity-based credentials while the identity provider retains verification and communication with the service provider via Security Assertion Mark Up Language. Thanks to the standardized federated systems in the German higher education domain, the solution not only enables a smooth transition to self-sovereign identities but can also be easily transferred to other universities using the same federated identity framework.

We consider the problem of computing k shortest paths in a two-dimensional environment with polygonal obstacles, where the jth path, for 1 ≤ j ≤ k, is the shortest path in the free space that is also homotopically distinct from each of the first j – 1 paths. In fact, we consider a more general problem: given a source point s, construct a partition of the free space, called the kth shortest path map (k-SPM), in which the homotopy of the kth shortest path in a region has the same structure. Our main combinatorial result establishes a tight bound of Θ(k2h + kn) on the worst-case complexity of this map. We also describe an O((k3h + k2n) log (kn)) time algorithm for constructing the map. In fact, the algorithm constructs the jth map for every j ≤ k. Finally, we present a simple visibility-based algorithm for computing the k shortest paths between two fixed points. This algorithm runs in O(m log n + k) time and uses O(m + k) space, where m is the size of the visibility graph. This latter algorithm can be extended to compute k shortest simple (non-self-intersecting) paths, taking O(k2 m(m + kn) log (kn)) time. We invite the reader to play with our applet demonstrating k-SPMs [10].

Space–time block coding (STBC) orthogonal frequency division multiplexing (OFDM) is known to improve the reliability of broadband communication over wireless links. However, this technique suffers from a performance loss when the multiple‐input multiple‐output (MIMO) channel is correlated. This study addresses this problem. A STBC‐OFDM system is proposed that is based on convolution that is skew‐circular, rather than circular. This skew‐circular convolution leads to one additional degree of freedom. The additional parameter can be optimised leading to improved performance for MIMO channels that are correlated. The skew‐circular convolution is achieved via the introduction of a generalised prefix. The simulation results are given, illustrating the performance improvement of the proposed STBC‐OFDM system. Furthermore, the proposed system is shown to be robust when channel state information is known not precisely, but imperfectly.

We propose an algorithm for the problem of computing shortest paths among curved obstacles in the plane. If the obstacles have O(n) description complexity, then the algorithm runs in O(n log n) time plus a term dependent on the properties of the boundary arcs. Specifically, if the arcs allow a certain kind of bisector intersection to be computed in constant time, or even in O(log n) time, then the running time of the overall algorithm is O(n log n). If the arcs support only constant-time tangent, intersection, and length queries, as is customarily assumed, then the algorithm computes an approximate shortest path, with relative error ε, in time O(n log n + n log 1/ε). In fact, the algorithm computes an approximate shortest path map, a data structure with O(n log n) size, that allows it to report the (approximate) length of a shortest path from a fixed source point to any query point in the plane in O(log n) time.

A well-known problem in computational geometry is Klee's measure problem, which asks for the volume of a union of axis-aligned boxes in d-space. In this paper, we consider Klee's measure problem for the special case where a 2-dimensional orthogonal projection of all the boxes has a common corner. We call such a set of boxes 2-grounded and, more generally, a set of boxes is k-grounded if in a k-dimensional orthogonal projection they share a common corner. Our main result is an O(n(d-1)/2log2n) time algorithm for computing Klee's measure for a set of n 2-grounded boxes. This is an improvement of roughly O(√n) compared to the fastest solution of the general problem. The algorithm works for k-grounded boxes, for any k ≥ 2, and in the special case of k=d, also called the hypervolume indicator problem, the time bound can be improved further by a log n factor. The key idea of our technique is to reduce the d-dimensional problem to a semi-dynamic weighted volume problem in dimension d-2. The weighted volume problem requires solving a combinatorial problem of maintaining the sum of ordered products, which may be of independent interest.