Related papers: Integer and Unsplittable Multiflows in Series-Para…
The one-way measurement model is a framework for universal quantum computation, in which algorithms are partially described by a graph G of entanglement relations on a collection of qubits. A sufficient condition for an algorithm to perform…
Tutte conjectured in 1972 that every 4-edge connected graph has a nowhere-zero 3-flow. This has long been known to be equivalent to the conjecture that every 5-regular 4-edge-connected graph has an edge orientation in which every out-degree…
Coflow is a recently proposed network abstraction to capture communication patterns in data centers. The coflow scheduling problem in large data centers is one of the most important $NP$-hard problems. Previous research on coflow scheduling…
In this work we consider a generalization of graph flows. A graph flow is, in its simplest formulation, a labeling of the directed edges with real numbers subject to various constraints. A common constraint is conservation in a vertex,…
We investigate multidimensional nowhere-zero flows of bridgeless graphs. By extending the established use of the Euclidean norm, this paper considers the Manhattan and Chebyshev norms, leading to the definition of the flow numbers…
We are interested in how to best communicate a (usually real valued) source to a number of destinations (sinks) over a network with capacity constraints in a collective fidelity metric over all the sinks, a problem which we call joint…
Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…
The famous flow decomposition theorem of Gallai (1985) states that any static edge $s$,$d$-flow in a directed graph can be decomposed into a nonnegative linear combination of incidence vectors of paths and cycles. In this paper, we study…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
The flow semigroup, introduced by John Rhodes, is an invariant for digraphs and a complete invariant for graphs. After collecting together previous partial results, we refine and prove Rhodes's conjecture on the structure of the maximal…
This article grew out of the urge to realize explicit examples of solutions for the Ricci flow as families of isometrically embedded submanifolds, together with its Gromov-Hausdorff collapses. To this aim, we consider the Ricci flow of…
We present a framework for modeling complex, high-dimensional distributions on convex polytopes by leveraging recent advances in discrete and continuous normalizing flows on Riemannian manifolds. We show that any full-dimensional polytope…
In 1983, Bouchet conjectured that every flow-admissible signed graph admits a nowhere-zero 6-flow. We verify this conjecture for the class of flow-admissible signed graphs possessing a spanning even Eulerian subgraph, which includes as a…
We establish uniqueness and structural stability of a class of parallel flows in a 2D straight, infinite channel, under perturbations with either globally or locally bounded Dirichlet integrals. The significant feature of our result is that…
A computational flow is a pair consisting of a sequence of computational problems of a certain sort and a sequence of computational reductions among them. In this paper we will develop a theory for these computational flows and we will use…
In this paper, we prove a tight minimum degree condition in general graphs for the existence of paths between two given endpoints, whose lengths form a long arithmetic progression with common difference one or two. This allows us to obtain…
The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a $1-\epsilon$ approximation to the multicommodity flow problem on graphs is a well-studied problem.…
We consider general, steady, balanced flows of a commodity over a network where an instance of the network flow is characterized by edge flows and nodal potentials. Edge flows in and out of a node are assumed to be conserved, thus…
This paper concerns a generalization of nowhere-zero modular q-flows from graphs to simplicial complexes of dimension d greater than 1. A modular q-flow of a simplicial complex is an element of the kernel of the d-th boundary map with…
In a digraph, a dicut is a cut where all the arcs cross in one direction. A dijoin is a subset of arcs that intersects each dicut. Woodall conjectured in 1976 that in every digraph, the minimum size of a dicut equals to the maximum number…