Related papers: Finding Diverse Trees, Paths, and More
One of the most important questions in matroid optimization is to find disjoint common bases of two matroids. The significance of the problem is well-illustrated by the long list of conjectures that can be formulated as special cases.…
In this paper, we study the complexity of the periodic temporal graph realization problem with respect to upper bounds on the fastest path durations among its vertices. This constraint with respect to upper bounds appears naturally in…
We argue that parameterized complexity is a useful tool with which to study global constraints. In particular, we show that many global constraints which are intractable to propagate completely have natural parameters which make them…
An important question in the study of constraint satisfaction problems (CSP) is understanding how the graph or hypergraph describing the incidence structure of the constraints influences the complexity of the problem. For binary CSP…
The MULTICUT problem, given a graph G, a set of terminal pairs T={(s_i,t_i) | 1 <= i <= r} and an integer p, asks whether one can find a cutset consisting of at most p non-terminal vertices that separates all the terminal pairs, i.e., after…
We give a fixed-parameter tractable algorithm that, given a parameter $k$ and two graphs $G_1,G_2$, either concludes that one of these graphs has treewidth at least $k$, or determines whether $G_1$ and $G_2$ are isomorphic. The running time…
We study the following general disjoint paths problem: given a supply graph $G$, a set $T\subseteq V(G)$ of terminals, a demand graph $H$ on the vertices $T$, and an integer $k$, the task is to find a set of $k$ pairwise vertex-disjoint…
Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and…
A probabilistic representation for initial value semilinear parabolic problems based on generalized random trees has been derived. Two different strategies have been proposed, both requiring generating suitable random trees combined with a…
A natural way to deal with multiple, partially conflicting objectives is turning all the objectives but one into budget constraints. Some classical polynomial-time optimization problems, such as spanning tree and forest, shortest path,…
Due to the limitation on computational power of existing computers, the polynomial time does not works for identifying the tractable problems in big data computing. This paper adopts the sublinear time as the new tractable standard to…
The Longest Path Problem is a question of finding the maximum length between pairs of vertices of a graph. In the general case, the problem is NP-complete. However, there is a small collection of graph classes for which there exists an…
Tree-shaped graphical models are widely used for their tractability. However, they unfortunately lack expressive power as they require committing to a particular sparse dependency structure. We propose a novel class of generative models…
Structural decomposition methods have been developed for identifying tractable classes of instances of fundamental problems in databases, such as conjunctive queries and query containment, of the constraint satisfaction problem in…
Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning…
The notion of resolving sets in a graph was introduced by Slater (1975) and Harary and Melter (1976) as a way of uniquely identifying every vertex in a graph. A set of vertices in a graph is a resolving set if for any pair of vertices x and…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
Maximum diversity problems arise in many practical settings from facility location to social networks, and constitute an important class of NP-hard problems in combinatorial optimization. There has been a growing interest in these problems…
This paper deals with the recoverable robust spanning tree problem under interval uncertainty representations. A polynomial time, combinatorial algorithm for the recoverable spanning tree problem is first constructed. This problem…
Given a graph $G$, and terminal vertices $s$ and $t$, the TRACKING PATHS problem asks to compute a minimum number of vertices to be marked as trackers, such that the sequence of trackers encountered in each s-t path is unique. TRACKING…