We study different symbolic algorithms to solve two related reconfiguration problems on graphs: the token swapping problem and the permutation routing via matchings problem. Input to both problems is a connected graph with labeled vertices and a token in e ...
A faithful (unit) distance graph in R-d is a graph whose set of vertices is a finite subset of the d-dimensional Euclidean space, where two vertices are adjacent if and only if the Euclidean distance between them is exactly 1. A (unit) distance graph in Rd ...
Cut and spectral sparsification of graphs have numerous applications, including e.g. speeding up algorithms for cuts and Laplacian solvers. These powerful notions have recently been extended to hypergraphs, which are much richer and may offer new applicati ...
Let G be a drawing of a graph with n vertices and e > 4n edges, in which no two adjacent edges cross and any pair of independent edges cross at most once. According to the celebrated Crossing Lemma of Ajtai, Chvatal, Newborn, Szemeredi and Leighton, the nu ...
We present a factors 4/3 approximation algorithm for the problem of finding a minimum 2-edge connected spanning subgraph of a given undirected multigraph. The algorithm is based upon a reduction to a restricted class of graphs. In these graphs, the approxi ...
An apparatus can include a congestion controller at a source endpoint node of a network that is configured to send substantially real-time media data at a variable sending rate to another endpoint node via the network. The congestion controller can be conf ...
We present a framework for approximating the metric TSP based on a novel use of matchings. Traditionally, matchings have been used to add edges to make a given graph Eulerian, whereas our approach also allows for the removal of certain edges leading to a d ...
We compute the motivic Donaldson-Thomas invariants of the one-loop quiver, with an arbitrary potential. This is the first computation of motivic Donaldson-Thomas invariants to use in an essential way the full machinery of (mu) over cap -equivariant motives ...
We show how any labeled convex polygon associated to a compact semi-toric system, as de fined by V (u) over tilde Ngoc, determines Karshon's labeled directed graph which classifies the underlying Hamiltonian S-1-space up to isomorphism. Then we characteriz ...
