Related papers: A Polynomial Time Approximation Algorithm for the …
We present a nearly-linear time algorithm for finding a minimum-cost flow in planar graphs with polynomially bounded integer costs and capacities. The previous fastest algorithm for this problem is based on interior point methods (IPMs) and…
We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of $n$ data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the…
We study a wholesale supply chain ordering problem. In this problem, the supplier has an initial stock, and faces an unpredictable stream of incoming orders, making real-time decisions on whether to accept or reject each order. What makes…
We study the computational complexity of the map redistricting problem (gerrymandering). Mathematically, the electoral district designer (gerrymanderer) attempts to partition a weighted graph into $k$ connected components (districts) such…
The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed…
We revisit two NP-hard geometric partitioning problems - convex decomposition and surface approximation. Building on recent developments in geometric separators, we present quasi-polynomial time algorithms for these problems with improved…
We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…
We study the general scheduling problem (GSP) which generalizes and unifies several well-studied preemptive single-machine scheduling problems, such as weighted flow time, weighted sum of completion time, and minimizing the total weight of…
We consider a special case of the ordinary NP-hard two-machine flow shop problem with the objective of determining simultaneously a minimal common due date and the minimal number of tardy jobs. In [S. S. Panwalkar, C. Koulamas, An O(n^2)…
We study optimization problems that are neither approximable in polynomial time (at least with a constant factor) nor fixed parameter tractable, under widely believed complexity assumptions. Specifically, we focus on Maximum Independent…
In this work, we study the classic submodular maximization problem under knapsack constraints and beyond. We first present an $(7/16-\varepsilon)$-approximate algorithm for single knapsack constraint, which requires…
In the paper we consider the problem of scheduling $n$ identical jobs on 4 uniform machines with speeds $s_1 \geq s_2 \geq s_3 \geq s_4,$ respectively. Our aim is to find a schedule with a minimum possible length. We assume that jobs are…
We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling…
We consider the following two deterministic inventory optimization problems over a finite planning horizon $T$ with non-stationary demands. (a) Submodular Joint Replenishment Problem: This involves multiple item types and a single retailer…
In this paper, we begin the exploration of vertex-ordering problems through the lens of exponential-time approximation algorithms. In particular, we ask the following question: Can we simultaneously beat the running times of the fastest…
We study the problem of scheduling jobs on parallel machines minimizing the total completion time, with each job using exactly one resource. First, we derive fundamental properties of the problem and show that the problem is polynomially…
The stochastic knapsack problem is the stochastic variant of the classical knapsack problem in which the algorithm designer is given a a knapsack with a given capacity and a collection of items where each item is associated with a profit…
We study a delay-sensitive information flow problem where a source streams information to a sink over a directed graph G(V,E) at a fixed rate R possibly using multiple paths to minimize the maximum end-to-end delay, denoted as the…
Given a bidirected ring with capacities and a demand graph, we present an approximation algorithm to the problem of finding the minimum $\alpha$ such that there exists a feasible unsplittable routing of the demands after multiplying each…
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…