Related papers: Online unit clustering in higher dimensions
Cardinality constrained bin packing or bin packing with cardinality constraints is a basic bin packing problem. In the online version with the parameter k \geq 2, items having sizes in (0,1] associated with them are presented one by one to…
Given a weighted and complete graph G = (V, E), V denotes the set of n objects to be clustered, and the weight d(u, v) associated with an edge (u, v) belonging to E denotes the dissimilarity between objects u and v. The diameter of a…
We study a competitive online optimization problem with multiple inventories. In the problem, an online decision maker seeks to optimize the allocation of multiple capacity-limited inventories over a slotted horizon, while the allocation…
We analyze the competitive ratio and the advice complexity of the online unbounded knapsack problem. An instance is given as a sequence of n items with a size and a value each, and an algorithm has to decide how often to pack each item into…
This paper is devoted to the online dominating set problem and its variants. We believe the paper represents the first systematic study of the effect of two limitations of online algorithms: making irrevocable decisions while not knowing…
We consider the online vector packing problem in which we have a $d$ dimensional knapsack and items $u$ with weight vectors $\mathbf{w}_u \in \mathbb{R}_+^d$ arrive online in an arbitrary order. Upon the arrival of an item, the algorithm…
Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…
In this paper, we study two variants of the online metric matching problem. The first problem is the online metric matching problem where all the servers are placed at one of two positions in the metric space. We show that a simple greedy…
Clustering algorithms aim to organize data into groups or clusters based on the inherent patterns and similarities within the data. They play an important role in today's life, such as in marketing and e-commerce, healthcare, data…
Let $(X, d)$ be a metric space and $C \subseteq 2^X$ -- a collection of special objects. In the $(X,d,C)$-chasing problem, an online player receives a sequence of online requests $\{B_t\}_{t=1}^T \subseteq C$ and responds with a trajectory…
In this paper, we consider the online version of the machine minimization problem (introduced by Chuzhoy et al., FOCS 2004), where the goal is to schedule a set of jobs with release times, deadlines, and processing lengths on a minimum…
We study the relationship between the competitive ratio and the tail distribution of randomized online minimization problems. To this end, we define a broad class of online problems that includes some of the well-studied problems like…
We are given a set $P$ of $n$ points in the plane, and a sequence of axis-aligned squares that arrive in an online fashion. The online hitting set problem consists of maintaining, by adding new points if necessary, a set $H\subseteq P$ that…
In this paper, we exploit linear programming duality in the online setting (i.e., where input arrives on the fly) from the unique perspective of designing lower bounds on the competitive ratio. In particular, we provide a general technique…
In this paper, we consider the online vertex-weighted bipartite matching problem in the random arrival model. We consider the generalization of the RANKING algorithm for this problem introduced by Huang, Tang, Wu, and Zhang (TALG 2019), who…
The online bisection problem requires maintaining a dynamic partition of $n$ nodes into two equal-sized clusters. Requests arrive sequentially as node pairs. If the nodes lie in different clusters, the algorithm pays unit cost. After each…
Online matching and its variants are some of the most fundamental problems in the online algorithms literature. In this paper, we study the online weighted bipartite matching problem. Karp et al. (STOC 1990) gave an elegant algorithm in the…
This paper shows that one can be competitive with the k-means objective while operating online. In this model, the algorithm receives vectors v_1,...,v_n one by one in an arbitrary order. For each vector the algorithm outputs a cluster…
We study online convex optimization in a setting where the learner seeks to minimize the sum of a per-round hitting cost and a movement cost which is incurred when changing decisions between rounds. We prove a new lower bound on the…
In the online multiple knapsack problem, an algorithm faces a stream of items, and each item has to be either rejected or stored irrevocably in one of $n$ bins (knapsacks) of equal size. The gain of an~algorithm is equal to the sum of sizes…