We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes and the goal is to find a smallest subset of non-terminal nodes (edges) to delete so that the terminal nodes do not have an odd length path between them. In an earlier work, Lokshtanov and Ramanujan showed that both odd multiway node cut and odd multiway edge cut are ...

We present a deterministic algorithm that computes the edge-connectivity of a graph in near-linear time. This is for a simple undirected unweighted graph G with n vertices and m edges. This is the first o(mn) time deterministic algorithm for the problem. Our algorithm is easily extended to find a concrete minimum edge-cut. In fact, we can construct the classic cactus representation of all minim...

Given a directed graph G, a set of k terminals and an integer p, the Directed Vertex Multiway Cut problem asks if there is a set S of at most p (nonterminal) vertices whose removal disconnects each terminal from all other terminals. Directed Edge Multiway Cut is the analogous problem where S is a set of at most p edges. These two problems indeed are known to be equivalent. A natural generalizat...

Motivated by applications from computer network security and software engineering, we study the problem of reducing reachability on a graph with unknown edge costs. When the costs are known, reachability reduction can be solved using a linear relaxation of sparsest cut. Problems arise, however, when edge costs are unknown. In this case, blindly applying sparsest cut with incorrect edge costs ca...

Efficient polynomial time algorithms are well known for the minimum spanning tree problem. However, given an undirected graph with integer edge weights, minimum spanning trees may not be unique. In this article, we present an algorithm that lists all the minimum spanning trees included in the graph. The computational complexity of the algorithm is O(N(mn+ n2 log n)) in time and O(m) in space, w...

We propose a fixed-parameter tractable algorithm for the Max-Cut problem on embedded 1-planar graphs parametrized by the crossing number k of the given embedding. A graph is called 1-planar if it can be drawn in the plane with at most one crossing per edge. Our algorithm recursively reduces a 1-planar graph to at most 3 planar graphs, using edge removal and node contraction. The Max-Cut problem...

An edge cut W of a connected graph G is a k-restricted edge cut if G−W is disconnected, and every component of G −W has at least k vertices. The k-restricted edge connectivity is defined as the minimum cardinality over all k-restricted edge cuts. A permutation graph is obtained by taking two disjoint copies of a graph and adding a perfect matching between the two copies. The k-restricted edge c...

For a large class of irregular mesh applications, the structure of the mesh changes from one phase of the computation to the next. Eventually, as the mesh evolves, the adapted mesh has to be repartitioned to ensure good load balance. If this new graph is partitioned from scratch, it may lead to an excessive migration of data among processors. In this paper, we present schemes for computing repa...

Let K be an abelian group and G be a connected graph, both finite. Using basic properties of circulations, we show that it is easy to generate uniformly random K-circulations on G. This leads to efficient algorithms for computing the cut edges, cut edge-pairs, and cut vertices of a graph; for example, the cut edges are “usually” the edges where a random circulation vanishes. In the distributed ...

Recently, attempts were made to generalize the undirected branching greedoid to a greedoid whose feasible sets consist of sets of edges containing the root satisfying additional size restrictions. Although this definition does not always result in a greedoid, the lift of the undirected branching greedoid has the properties desired by the authors. The k-th lift of a greedoid has sets whose nulli...