Related papers: Improved and Parameterized Algorithms for Online M…
Clustering is a fundamental problem, aiming to partition a set of elements, like agents or data points, into clusters such that elements in the same cluster are closer to each other than to those in other clusters. In this paper, we present…
In the Tree Augmentation Problem (TAP) the goal is to augment a tree $T$ by a minimum size edge set $F$ from a given edge set $E$ such that $T \cup F$ is $2$-edge-connected. The best approximation ratio known for TAP is $1.5$. In the more…
In the online metric matching problem, $n$ servers and $n$ requests lie in a metric space. Servers are available upfront, and requests arrive sequentially. An arriving request must be matched immediately and irrevocably to an available…
We study the problem of online Multi-Agent Pickup and Delivery (MAPD), where a team of agents must repeatedly serve dynamically appearing tasks on a shared map. Existing online methods either rely on simple heuristics, which result in poor…
In this paper, we introduce the problem of Online Matching with Delays and Size-based Costs (OMDSC). The OMDSC problem involves $m$ requests arriving online. At any time, a group can be formed by matching any number of these requests that…
The data arrangement problem on regular trees (DAPT) consists in assigning the vertices of a given graph G to the leaves of a d-regular tree T such that the sum of the pairwise distances of all pairs of leaves in T which correspond to edges…
Resource allocation in distributed and networked systems such as the Cloud is becoming increasingly flexible, allowing these systems to dynamically adjust toward the workloads they serve, in a demand-aware manner. Online balanced…
The minimum height of vertex and edge partition trees are well-studied graph parameters known as, for instance, vertex and edge ranking number. While they are NP-hard to determine in general, linear-time algorithms exist for trees.…
Retrieval-augmented generation (RAG) systems face significant challenges in multi-hop question answering (MHQA), where complex queries require synthesizing information across multiple document chunks. Existing approaches typically rely on…
We study the performance of a best reply algorithm for online resource allocation problems with a diseconomy of scale. In an online resource allocation problem, we are given a set of resources and a set of requests that arrive in an online…
The Virtual Network Embedding Problem (VNEP) captures the essence of many resource allocation problems of today's infrastructure providers, which offer their physical computation and networking resources to customers. Customers request…
In this paper, we investigate the weighted tree augmentation problem (TAP), where the goal is to augment a tree with a minimum cost set of edges such that the graph becomes two edge connected. First we show that in weighted TAP, we can…
The performance of distributed and data-centric applications often critically depends on the interconnecting network. Applications are hence modeled as virtual networks, also accounting for resource demands on links. At the heart of…
Motivated primarily by applications in cloud computing, we study a simple, yet powerful, online allocation problem in which jobs of varying durations arrive over continuous time and must be assigned immediately and irrevocably to one of the…
Large Language Models (LLMs) are increasingly deployed in both latency-sensitive online services and cost-sensitive offline workloads. Co-locating these workloads on shared serving instances can improve resource utilization, but directly…
We introduce a class of budgeted prize-collecting covering subgraph problems. For an input graph with prizes on the vertices and costs on the edges, the aim of these problems is to find a connected subgraph such that the cost of its edges…
We consider the Connectivity Augmentation Problem (CAP), a classical problem in the area of Survivable Network Design. It is about increasing the edge-connectivity of a graph by one unit in the cheapest possible way. More precisely, given a…
The Minimum Linear Arrangement problem (MLA) consists of finding a mapping $\pi$ from vertices of a graph to distinct integers that minimizes $\sum_{\{u,v\}\in E}|\pi(u) - \pi(v)|$. In that setting, vertices are often assumed to lie on a…
In this paper, the cooperative jobs dispatching problem in an edge computing network with multiple access points (APs) and edge servers is considered. Due to the uncertain traffic in the network between APs and edge servers, the job…
We initiate the study of online problems with set delay, where the delay cost at any given time is an arbitrary function of the set of pending requests. In particular, we study the online min-cost perfect matching with set delay (MPMD-Set)…