Related papers: An Output-Polynomial Time Algorithm to Determine a…
We consider the problem of Data Flow Analysis over monotone data flow frameworks with a finite lattice. The problem of computing the Maximum Fixed Point (MFP) solution is shown to be P-complete even when the lattice has just four elements.…
In data-parallel computing frameworks, intermediate parallel data is often produced at various stages which needs to be transferred among servers in the datacenter network (e.g. the shuffle phase in MapReduce). A stage often cannot start or…
An important objective in scheduling literature is to minimize the sum of weighted flow times. We are given a set of jobs where each job is characterized by a release time, a processing time, and a weight. Our goal is to find a preemptive…
We consider a large family of problems in which an ordering (or, more precisely, a chain of subsets) of a finite set must be chosen to minimize some weighted sum of costs. This family includes variations of Min Sum Set Cover (MSSC), several…
We provide evidence that computing the maximum flow value between every pair of nodes in a directed graph on $n$ nodes, $m$ edges,and capacities in the range $[1..n]$, which we call the All-Pairs Max-Flow problem, cannot be solved in time…
We classify, according to their computational complexity, integer optimization problems whose constraints and objective functions are polynomials with integer coefficients and the number of variables is fixed. For the optimization of an…
We are given a set of $n$ jobs that have to be executed on a set of $m$ speed-scalable machines that can vary their speeds dynamically using the energy model introduced in [Yao et al., FOCS'95]. Every job $j$ is characterized by its release…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By…
The problem of verifying multi-threaded execution against the memory consistency model of a processor is known to be an NP hard problem. However polynomial time algorithms exist that detect almost all failures in such execution. These are…
We extend the well known bottleneck paths problem in two directions for directed unweighted (unit edge cost) graphs with positive real edge capacities. Firstly we narrow the problem domain and compute the bottleneck of the entire network in…
This paper concerns the problem of multi-object tracking based on the min-cost flow (MCF) formulation, which is conventionally studied as an instance of linear program. Given its computationally tractable inference, the success of MCF…
We study a general class of bicriteria network design problems. A generic problem in this class is as follows: Given an undirected graph and two minimization objectives (under different cost functions), with a budget specified on the first,…
We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…
The massive integration of distributed energy resources changes the operational demands of the electric power distribution system, motivating optimization-based approaches. The added computational complexities of the resulting optimal power…
The multicommodity flow problem is NP-hard already for two commodities over bipartite graphs. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the surprising…
We consider an undirected graph $G = (VG, EG)$ with a set $T \subseteq VG$ of terminals, and with nonnegative integer capacities $c(v)$ and costs $a(v)$ of nodes $v\in VG$. A path in $G$ is a \emph{$T$-path} if its ends are distinct…
The Optimal Power Flow (OPF) problem is integral to the functioning of power systems, aiming to optimize generation dispatch while adhering to technical and operational constraints. These constraints are far from straightforward; they…
This work aims to introduce the framework of polynomial optimization theory to solve fractional polynomial problems (FPPs). Unlike other widely used optimization frameworks, the proposed one applies to a larger class of FPPs, not…