Related papers: Quasi-PTAS for Scheduling with Precedences using L…
We consider the general polynomial optimization problem $P: f^*=\min \{f(x)\,:\,x\in K\}$ where $K$ is a compact basic semi-algebraic set. We first show that the standard Lagrangian relaxation yields a lower bound as close as desired to the…
We study ordinal makespan scheduling on small numbers of identical machines, with respect to two parallel solutions. In ordinal scheduling, it is known that jobs are sorted by non-increasing sizes, but the specific sizes are not known in…
This paper provides three nearly-optimal algorithms for scheduling $t$ jobs in the $\mathsf{CLIQUE}$ model. First, we present a deterministic scheduling algorithm that runs in $O(\mathsf{GlobalCongestion} + \mathsf{dilation})$ rounds for…
Modern platforms are using accelerators in conjunction with standard processing units in order to reduce the running time of specific operations, such as matrix operations, and improve their performance. Scheduling on such hybrid platforms…
Consider a problem in which $n$ jobs that are classified into $k$ types arrive over time at their release times and are to be scheduled on a single machine so as to minimize the maximum flow time. The machine requires a setup taking $s$…
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
Learning-augmented algorithms have emerged as a powerful paradigm to surpass traditional worst-case lower bounds by integrating potentially noisy predictions. While this framework has seen success in online scheduling, existing work…
The non-clairvoyant scheduling problem has gained new interest within learning-augmented algorithms, where the decision-maker is equipped with predictions without any quality guarantees. In practical settings, access to predictions may be…
We present novel randomized approximation schemes for the Edit Distance (ED) problem and the Longest Common Subsequence (LCS) problem that, for any constant $\epsilon>0$, compute a $(1+\epsilon)$-approximation for ED and a…
We introduce and study a general scheduling problem that we term the Packing Scheduling problem. In this problem, jobs can have different arrival times and sizes; a scheduler can process job $j$ at rate $x_j$, subject to arbitrary packing…
We consider the online resource minimization problem in which jobs with hard deadlines arrive online over time at their release dates. The task is to determine a feasible schedule on a minimum number of machines. We rigorously study this…
Personnel scheduling problems have received considerable academic attention due to their relevance in various real-world applications. These problems involve preparing feasible schedules for an organization's employees and often account for…
We consider the problem of scheduling $n$ jobs to minimize the makespan on $m$ unrelated machines, where job $j$ requires time $p_{ij}$ if processed on machine $i$. A classic algorithm of Lenstra et al. yields the best known approximation…
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 consider the rooted orienteering problem in Euclidean space: Given $n$ points $P$ in $\mathbb R^d$, a root point $s\in P$ and a budget $\mathcal B>0$, find a path that starts from $s$, has total length at most $\mathcal B$, and visits as…
The NP-hard maximum value preordering problem is both a joint relaxation and a hybrid of the clique partition problem (a clustering problem) and the partial ordering problem. Toward approximate solutions and lower bounds, we introduce a…
We consider the following single-machine scheduling problem, which is often denoted $1||\sum f_{j}$: we are given $n$ jobs to be scheduled on a single machine, where each job $j$ has an integral processing time $p_j$, and there is a…
We consider the problem of scheduling multiprocessor jobs to minimize the total completion time under the given energy budget. Each multiprocessor job requires more than one processor at the same moment of time. Processors may operate at…
We consider several combinatorial optimization problems which combine the classic shop scheduling problems, namely open shop scheduling or job shop scheduling, and the shortest path problem. The objective of the obtained problem is to…
We approximate the backward reachable set of discrete-time autonomous polynomial systems using the recently developed occupation measure approach. We formulate the problem as an infinite-dimensional linear programming (LP) problem on…