To effectively sort and present relevant information pieces (e.g., answers, passages, documents) to human users, information systems rely on ranking models. Existing ranking models are typically designed for a specific task and therefore are not effective for complex information systems that require component changes or domain adaptations. For example, in the final stage of question answering, ...

Given a spatio-temporal network, a source, a destination, and a start-time interval, the All-start-time Lagrangian Shortest Paths (ALSP) problem determines a path set which includes the shortest path for every start time in the given interval. ALSP is important for critical societal applications related to air travel, road travel, and other spatiotemporal networks. However, ALSP is computationa...

A k-ranking of a graph G is a colouring φ : V (G) → {1, . . . , k} such that any path in G with endvertices x, y fulfilling φ(x) = φ(y) contains an internal vertex z with φ(z) > φ(x). On-line ranking number χ∗ r (G) of a graph G is a minimum k such that G has a k-ranking constructed step by step if vertices of G are coming and coloured one by one in an arbitrary order; when colouring a vertex, ...

In this paper we study the complexity of the problems: given a loop, described by linear constraints over a finite set of variables, is there a linear or lexicographical-linear ranking function for this loop? While existence of such functions implies termination, these problems are not equivalent to termination. When the variables range over the rationals (or reals), it is known that both probl...

An edge-ranking of a graph G is a labeling of the edges of G with positive integers such that every path between two edges with the same label γ contains an edge with label λ > γ. In the on-line edge-ranking model the edges e1, e2 . . . , em arrive one at a time in any order, where m is the number of edges in the graph. Only the partial information in the induced subgraph G[{e1, e2, . . . , ei}...

Heterogeneous graph based information recommendation have been proved useful in recent studies. Given a heterogeneous graph scheme, there are many possible meta paths between the query node and the result node, and each meta path addresses a hypothesis-based ranking function. In prior researches, meta paths are manually selected by domain experts. However, when the graph scheme becomes complex,...

A node ranking of a graph G = (V,E) is a proper node coloring C : V → N such that any path in G with end nodes x, y fulfilling C(x) = C(y) contains an internal node z with C(z) > C(x). In the on-line version of the node ranking problem, the nodes v1, v2, ..., vn are coming one by one in an arbitrary order; and only the edges of the induced subgraph G[{v1, v2, ..., vi}] are known when the color ...

A node k-ranking of a graph G = (V, E) is a proper node coloring C: V  {1, 2, ..., k} such that any path in G with end nodes x, y fulfilling C(x) = C(y) contains an internal node z with C(z) C(x). In the on-line version of this problem, the nodes v1, v2,..., vn are coming one by one in an arbitrary order; and only the edges of the induced subgraph G[{v1, v2, ..., vi}] are known when the color...

A vertex k-ranking of a simple graph is a coloring of its vertices with k colors in such a way that each path connecting two vertices of the same color contains a vertex with a bigger color. Consider the minimum vertex ranking spanning tree (MVRST) problem where the goal is to find a spanning tree of a given graph G which has a vertex ranking using the minimal number of colors over vertex ranki...