Related papers: Constrained Flows in Networks
We study a variant of Min Cost Flow in which the flow needs to be connected. Specifically, in the Connected Flow problem one is given a directed graph $G$, along with a set of demand vertices $D \subseteq V(G)$ with demands $\mathsf{dem}: D…
The power flow equations, which relate power injections and voltage phasors, are at the heart of many electric power system computations. While Newton-based methods typically find the "high-voltage" solution to the power flow equations,…
We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a…
We give the first O(m polylog(n)) time algorithms for approximating maximum flows in undirected graphs and constructing polylog(n) -quality cut-approximating hierarchical tree decompositions. Our algorithm invokes existing algorithms for…
In the last decade, algorithmic frameworks based on a structural graph parameter called mim-width have been developed to solve generally NP-hard problems. However, it is known that the frameworks cannot be applied to the Clique problem, and…
Given a directed graph $G = (V, E)$ with $n$ vertices, $m$ edges and a designated source vertex $s\in V$, we consider the question of finding a sparse subgraph $H$ of $G$ that preserves the flow from $s$ up to a given threshold $\lambda$…
A challenging problem in complex networks is the network reconstruction problem from data. This work deals with a class of networks denoted as conserved networks, in which a flow associated with every edge and the flows are conserved at all…
Network flows over time are a fascinating generalization of classical (static) network flows, introducing an element of time. They naturally model problems where travel and transmission are not instantaneous and flow may vary over time. Not…
In this paper we consider a defending problem on a network. In the model, the defender holds a total defending resource of R, which can be distributed to the nodes of the network. The defending resource allocated to a node can be shared by…
The GC problem is to identify a pre-determined number of center vertices such that the distances or costs from (or to) the centers to (or from) other vertices is minimized. The bottleneck of a path is the minimum capacity of edges on the…
In this paper we study information flow paths in a data network, where traffic generated by servers (or sources) takes a multi-hop path in order to reach its clients (destinations). Each node in the middle of this multi-hop path should…
Optimal power flow (OPF) is a critical optimization problem that allocates power to the generators in order to satisfy the demand at a minimum cost. Solving this problem exactly is computationally infeasible in the general case. In this…
Let $G=(V,E)$ be a graph with four distinguished vertices, two sources $s_1, s_2$ and two sinks $t_1,t_2$, let $c:\, E \rightarrow \mathbb Z_+$ be a capacity function, and let ${\cal P}$ be the set of all simple paths in $G$ from $s_1$ to…
We study the maximum $s,t$-flow oracle problem on planar directed graphs where the goal is to design a data structure answering max $s,t$-flow value (or equivalently, min $s,t$-cut value) queries for arbitrary source-target pairs $(s,t)$.…
Let $G = (VG, AG)$ be a directed graph with a set $S \subseteq VG$ of terminals and nonnegative integer arc capacities $c$. A feasible multiflow is a nonnegative real function $F(P)$ of "flows" on paths $P$ connecting distinct terminals…
Strong resilience properties of dynamical flow networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the inflow at a non-destination node gets split among its outgoing links is…
Several variants of the Constraint Satisfaction Problem have been proposed and investigated in the literature for modelling those scenarios where solutions are associated with some given costs. Within these frameworks computing an optimal…
Changing a given configuration in a graph into another one is known as a re- configuration problem. Such problems have recently received much interest in the context of algorithmic graph theory. We initiate the theoretical study of the…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
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…