We study the parameterized complexity of the directed variant of the classical Steiner Tree problem on various classes of directed sparse graphs. While the parameterized complexity of Steiner Tree parameterized by the number of terminals is well understood, not much is known about the parameterization by the number of non-terminals in the solution tree. All that is known for this parameterizati...

In recent years, there has been tremendous growth in the field of indoor and outdoor positioning sensors continuously producing huge volumes of trajectory data that has been used in many fields such as location-based services or location intelligence. Trajectory data is massively increased and semantically complicated, which poses a great challenge on spatio-temporal data indexing. This paper p...

Sumner’s universal tournament conjecture states that any tournament on 2n−2 vertices contains a copy of any directed tree on n vertices. We prove an asymptotic version of this conjecture, namely that any tournament on (2 + o(1))n vertices contains a copy of any directed tree on n vertices. In addition, we prove an asymptotically best possible result for trees of bounded degree, namely that for ...

There are applications which require the support of temporal data with branched time evolution, called branched-and-temporal data. In a branched-and-temporal database, both historic versions and current versions are allowed to be updated. We present an access method, the BTR-Tree, for branched-and-temporal databases with reasonable space and access time tradeoff. It is an index structure based ...

The minimum degree spanning tree problem has been studied extensively. In this paper, we present a polynomial time algorithm for the minimum degree spanning tree problem on directed acyclic graphs. The algorithm starts with an arbitrary spanning tree, and iteratively reduces the number of vertices of maximum degree. We can prove the algorithm must reduce a vertex of the maximum degree for each ...

Known results: • Generalizes Set Cover, (Non-Metric / Multi-level) Facility Location, Group Steiner Tree • Ω(log2− n)-hard (Halperin, Krauthgamer ’03) • |X| -apx in poly by sophisticated greedy algo (Zelikovsky ’97) • O(log |X|)-apx in nO(log |X|) time by more sophisticated greedy algo (Charikar, Chekuri, Cheung, Goel, Guha and Li ’99) • LP’s have integrality gap Ω( √ k) already for 5 layers; e...

Consider a directed graph G = (V,E) with n vertices and a root vertex r ∈ V . The DMDST problem for G is one of constructing a spanning tree rooted at r, whose maximal degree is the smallest among all such spanning trees. The problem is known to be NP-hard. A quasipolynomial time approximation algorithm for this problem is presented. The algorithm finds a spanning tree whose maximal degree is a...

A bidirected tree is the directed graph obtained from an undirected tree by replacing each undirected edge by two directed edges with opposite directions. Given a set of directed paths in a bidirected tree, the goal of the maximum edge-disjoint paths problem is to select a maximum-cardinality subset of the paths such that the selected paths are edge-disjoint. This problem can be solved optimall...