Related papers: A Combinatorial Algorithm for the Multi-commodity …
When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in the speed at which the LP can be solved, as it is linear in the number of constraints and variables. The…
This paper deals with the problem of computing, in an online fashion, a maximum benefit multi-commodity flow (\ONMCF), where the flow demands may be bigger than the edge capacities of the network. We present an online, deterministic,…
Throughput is a main performance objective in communication networks. This paper considers a fundamental maximum throughput routing problem -- the all-or-nothing multicommodity flow (ANF) problem -- in arbitrary directed graphs and in the…
We consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical…
In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum $s$-$t$ flow and maximum concurrent…
In many applications, uncertainty in problem data leads to the need for numerous computationally expensive simulations. This report addresses this challenge by developing a penalty-based ensemble algorithm. Building upon Jiang and Layton's…
We provide $m^{1+o(1)}k\epsilon^{-1}$-time algorithms for computing multiplicative $(1 - \epsilon)$-approximate solutions to multi-commodity flow problems with $k$-commodities on $m$-edge directed graphs, including concurrent…
We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give a polynomial time combinatorial…
The quantum approximate optimization algorithm (QAOA) is designed to determine optimum and near optimum solutions of quadratic (and higher order) unconstrained binary optimization (QUBO or HUBO) problems, which in turn accurately model…
In this paper, we prove a combinatorial property of flows on a cycle. $C(V,E)$ is an undirected cycle with two commodities: $\{s_{1},t_{1}\}, \{s_{2},t_{2}\}$;$r_1>0,r_2>0, \mathbf r=(r_i)_{i=1,2}$ and $f,f'$ are both feasible flows for…
We consider a generalization of the unsplittable maximum two-commodity flow problem on undirected graphs where each commodity $i\in{1,2}$ can be split into a bounded number $k_i$ of equally-sized chunks that can be routed on different…
In this paper we describe a new algorithm for buffered global routing according to a prescribed buffer site map. Specifically, we describe a provably good multi-commodity flow based algorithm that finds a global routing minimizing buffer…
We present a combinatorial method for the min-cost flow problem and prove that its expected running time is bounded by $\tilde O(m^{3/2})$. This matches the best known bounds, which previously have only been achieved by numerical algorithms…
We give the first local algorithm for computing multi-commodity flow and apply it to obtain a $(1+\epsilon)$-approximate algorithm for computing a $k$-commodity flow on an expander with $m$ edges in $(m+\epsilon^{-3}k^3D)n^{o(1)}$ time,…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
The chaotic nature of fluid flow and the uncertainties in initial conditions limit predictability. Small errors that occur in the initial condition can grow exponentially until they saturate at $\mathcal{O}$(1). Ensemble forecasting…
The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…
We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without…