Disjoint Paths is the problem of finding paths between given pairs of terminals in a graph such that no vertices are shared between paths. We analyze fixed-parameter tractability of several new Disjoint Paths-like routing problems motivated by congestion control in computer networks. In one model we are interested in finding paths between k pairs of terminals such that the first edge of each pa...

This work studies the edge-based representation of directed acyclic graphs, as well as the properties of recombination operators working on it. It is shown that this representation is not separable, and the structure of the basic information units that must be processed in order to maintain feasibility of the solutions is described. As an experimental analysis indicates, a recombination operato...

We are given an acyclic directed graph with one source, and a subset of its edges which contains exactly one outgoing edge for every non-sink vertex. These edges determine a unique path from the source to a sink. We can think of it as a switch in every vertex, which determines which way the water arriving to that vertex flows further. We are interested in determining either the sink the flow ar...

We present a simple algorithm which maintains the topological order of a directed acyclic graph with n nodes under an online edge insertion sequence in Õ(n) time, independent of the number of edges m inserted. For dense DAGs, this is an improvement over the previously best result of O(min{m 32 log n,m 32 +n log n}) by Katriel et al. We also provide an empirical comparison of our algorithm with ...

In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, first the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of ...

We describe DAGGER, an ab initio gene recognition program which combines the output of high dimensional signal sensors in an intuitive gene model based on directed acyclic graphs. In the first stage, candidate start, donor, acceptor, and stop sites are scored using the SNoW learning architecture. These sites are then used to generate a directed acyclic graph in which each source-sink path repre...

Link-independent and node-independent DAGs satisfy the property that any path from a source to the root on one DAG is link-disjoint (node-disjoint) with any path from the source to the root on the other DAG. To achieve resilient multipath routing, first introduce the concept of independent directed acyclic graphs (IDAGs). For a given a network, we develop polynomialtime algorithms to compute li...

We generalize chain enumeration in graded partially ordered sets by relaxing the graded, poset and Eulerian requirements. The resulting balanced digraphs, which include the classical Eulerian posets having an R-labeling, implies the existence of the (non-homogeneous) cd-index, a key invariant for studying inequalities for the flag vector of polytopes. Mirroring Alexander duality for Eulerian po...

We relate the search number of an undirected graph G with the minimum and maximum of the progressive pebble demands of the directed acyclic graphs obtained by orienting (7. Towards this end, we introduce node-searching, a slight variant of searching, in which an edge is cleared by placing searchers on both of its endpoints. We also show that the minimum number of searchers necessary to node-sea...

Proof. As the edges in GC represent causal relations, a path of length 0 (no edge) is not considered a causal relation, and existence of a directed path from a variable back to itself would contravene the causal DAG assumption, hence: irreflexive and acyclic (or, more accurate, asymmetric). Transitivity follows immediately, by concatenation, from the sequence 〈X, .., Y, .., Z〉, in which each no...