Related papers: Machine Covering in the Random-Order Model
In the Submodular Welfare Maximization (SWM) problem, the input consists of a set of $n$ items, each of which must be allocated to one of $m$ agents. Each agent $\ell$ has a valuation function $v_\ell$, where $v_\ell(S)$ denotes the welfare…
We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…
An effective technique for solving optimization problems over massive data sets is to partition the data into smaller pieces, solve the problem on each piece and compute a representative solution from it, and finally obtain a solution…
Motivated by applications in energy-efficient scheduling in data centers, Khuller, Li, and Saha introduced the {\em machine activation} problem as a generalization of the classical optimization problems of set cover and load balancing on…
This paper considers the basic problem of scheduling jobs online with preemption to maximize the number of jobs completed by their deadline on $m$ identical machines. The main result is an $O(1)$ competitive deterministic algorithm for any…
Efficient marketing or awareness-raising campaigns seek to recruit $n$ influential individuals -- where $n$ is the campaign budget -- that are able to cover a large target audience through their social connections. So far most of the…
In the online load balancing problem on related machines, we have a set of jobs (with different sizes) arriving online, and we need to assign each job to a machine immediately upon its arrival, so as to minimize the makespan, i.e., the…
We explore the machine-minimizing job scheduling problem, which has a rich history in the line of research, under an online setting. We consider systems with arbitrary job arrival times, arbitrary job deadlines, and unit job execution time.…
In a classical scheduling problem, we are given a set of $n$ jobs of unit length along with precedence constraints, and the goal is to find a schedule of these jobs on $m$ identical machines that minimizes the makespan. Using the standard…
In the Maximum Independent Set of Hyperrectangles problem, we are given a set of $n$ (possibly overlapping) $d$-dimensional axis-aligned hyperrectangles, and the goal is to find a subset of non-overlapping hyperrectangles of maximum…
We study a fundamental model of online preference aggregation, where an algorithm maintains an ordered list of $n$ elements. An input is a stream of preferred sets $R_1, R_2, \dots, R_t, \dots$. Upon seeing $R_t$ and without knowledge of…
For the classical maximum coverage problem, the greedy algorithm achieves a worst-case $1-1/e$ approximation, which is optimal unless $\text{P} = \text{NP}$. The notion of coverage appears in a wide range of optimization tasks, where…
Motivated by sequential budgeted allocation problems, we investigate online matching problems where connections between vertices are not i.i.d., but they have fixed degree distributions -- the so-called configuration model. We estimate the…
We consider the machine covering problem for selfish related machines. For a constant number of machines, m, we show a monotone polynomial time approximation scheme (PTAS) with running time that is linear in the number of jobs. It uses a…
A common approach for designing scalable algorithms for massive data sets is to distribute the computation across, say $k$, machines and process the data using limited communication between them. A particularly appealing framework here is…
A basic combinatorial online resource allocation problem is considered, where multiple servers have individual capacity constraints, and at each time slot, a set of jobs arrives, that have potentially different weights to different servers.…
We consider the problem of online preemptive scheduling on a single machine to minimize the total flow time. In clairvoyant scheduling, where job processing times are revealed upon arrival, the Shortest Remaining Processing Time (SRPT)…
In this paper we consider the online Submodular Welfare (SW) problem. In this problem we are given $n$ bidders each equipped with a general (not necessarily monotone) submodular utility and $m$ items that arrive online. The goal is to…
Online algorithms are usually analyzed using the notion of competitive ratio which compares the solution obtained by the algorithm to that obtained by an online adversary for the worst possible input sequence. Often this measure turns out…
We consider Online Minimum Bipartite Matching under the uniform metric. We show that Randomized Greedy achieves a competitive ratio equal to $(1+1/n) (H_{n+1}-1)$, which matches the lower bound. Comparing with the fact that RG achieves an…