Related papers: The Online $k$-Taxi Problem
The culture of sharing instead of ownership is sharply increasing in individuals behaviors. Particularly in transportation, concepts of sharing a ride in either carpooling or ridesharing have been recently adopted. An efficient optimization…
We consider the (exact, minimum) $k$-cut problem: given a graph and an integer $k$, delete a minimum-weight set of edges so that the remaining graph has at least $k$ connected components. This problem is a natural generalization of the…
This paper considers the classic Online Steiner Forest problem where one is given a (weighted) graph $G$ and an arbitrary set of $k$ terminal pairs $\{\{s_1,t_1\},\ldots ,\{s_k,t_k\}\}$ that are required to be connected. The goal is to…
For a positive integer $k \ge 1$, a $k$-star ($k^+$-star, $k^-$-star, respectively) is a connected graph containing a degree-$\ell$ vertex and $\ell$ degree-$1$ vertices, where $\ell = k$ ($\ell \ge k$, $1 \le \ell \le k$, respectively).…
We consider a variant of the online caching problem where the items exhibit dependencies among each other: an item can reside in the cache only if all its dependent items are also in the cache. The dependency relations can form any directed…
We study online task assignment problem with reusable resources, motivated by practical applications such as ridesharing, crowdsourcing and job hiring. In the problem, we are given a set of offline vertices (agents), and, at each time, an…
We consider the following online optimization problem. We are given a graph $G$ and each vertex of the graph is assigned to one of $\ell$ servers, where servers have capacity $k$ and we assume that the graph has $\ell \cdot k$ vertices.…
We consider the problem of enumerating optimal solutions for two hypergraph $k$-partitioning problems -- namely, Hypergraph-$k$-Cut and Minmax-Hypergraph-$k$-Partition. The input in hypergraph $k$-partitioning problems is a hypergraph…
We consider a the minimum k-way cut problem for unweighted graphs with a size bound s on the number of cut edges allowed. Thus we seek to remove as few edges as possible so as to split a graph into k components, or report that this requires…
This paper revisits the 2-approximation algorithm for $k$-MST presented by Garg in light of a recent paper of Paul et al.. In the $k$-MST problem, the goal is to return a tree spanning $k$ vertices of minimum total edge cost. Paul et al.…
We study the on-line minimum weighted bipartite matching problem in arbitrary metric spaces. Here, $n$ not necessary disjoint points of a metric space $M$ are given, and are to be matched on-line with $n$ points of $M$ revealed one by one.…
We consider the classical online scheduling problem P||C_{max} in which jobs are released over list and provide a nearly optimal online algorithm. More precisely, an online algorithm whose competitive ratio is at most (1+\epsilon) times…
In this work, we consider the $k$-Canadian Traveller Problem ($k$-CTP) under the learning-augmented framework proposed by Lykouris & Vassilvitskii. $k$-CTP is a generalization of the shortest path problem, and involves a traveller who knows…
We consider a vehicle routing problem which seeks to minimize cost subject to service level constraints on several groups of deliveries. This problem captures some essential challenges faced by a logistics provider which operates…
We consider the problem of learning and using predictions for warm start algorithms with predictions. In this setting, an algorithm is given an instance of a problem, and a prediction of the solution. The runtime of the algorithm is bounded…
In the $k$-cut problem, we are given an edge-weighted graph $G$ and an integer $k$, and have to remove a set of edges with minimum total weight so that $G$ has at least $k$ connected components. The current best algorithms are an…
In this paper, we study a very general type of online network design problem, and generalize two different previous algorithms, one for an online network design problem due to Berman and Coulston [4] and one for (offline) general network…
We study deterministic algorithms for computing graph cuts, with focus on two fundamental problems: balanced sparse cut and $k$-vertex connectivity for small $k$ ($k=O(\polylog n)$). Both problems can be solved in near-linear time with…
An online non-convex optimization problem is considered where the goal is to minimize the flow time (total delay) of a set of jobs by modulating the number of active servers, but with a switching cost associated with changing the number of…
We give algorithms for geometric graph problems in the modern parallel models inspired by MapReduce. For example, for the Minimum Spanning Tree (MST) problem over a set of points in the two-dimensional space, our algorithm computes a…