Related papers: Tight Bounds for Online Weighted Tree Augmentation
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…
We consider a perimeter defense problem in a rooted full tree graph environment in which a single defending vehicle seeks to defend a set of specified vertices, termed as the perimeter from mobile intruders that enter the environment…
Constructing the maximum spanning tree $T$ of an edge-weighted connected graph $G$ is one of the important research topics in computer science and optimization, and the related research results have played an active role in practical…
In the context of an efficient network traffic engineering process where the network continuously measures a new traffic matrix and updates the set of paths in the network, an automated process is required to quickly and efficiently…
The Secluded Path problem models a situation where a sensitive information has to be transmitted between a pair of nodes along a path in a network. The measure of the quality of a selected path is its exposure, which is the total weight of…
We consider the classic Set Cover problem in the data stream model. For $n$ elements and $m$ sets ($m\geq n$) we give a $O(1/\delta)$-pass algorithm with a strongly sub-linear $\tilde{O}(mn^{\delta})$ space and logarithmic approximation…
The weighted ancestor problem on a rooted node-weighted tree $T$ is a generalization of the classic predecessor problem: construct a data structure for a set of integers that supports fast predecessor queries. Both problems are known to…
Given a vertex-weighted connected graph $G = (V, E)$, the maximum weight internal spanning tree (MwIST for short) problem asks for a spanning tree $T$ of $G$ such that the total weight of the internal vertices in $T$ is maximized. The…
We initiate the study of degree-bounded network design problems in the online setting. The degree-bounded Steiner tree problem { which asks for a subgraph with minimum degree that connects a given set of vertices { is perhaps one of the…
In this paper, we consider the multi-level aggregation problem with deadlines (MLAPD) previously studied by Bienkowski et al. (2015), Buchbinder et al. (2017), and Azar and Touitou (2019). This is an online problem where the algorithm…
We prove that the local limit of the weighted spanning trees on any simple connected high degree almost regular sequence of electric networks is the Poisson(1) branching process conditioned to survive forever, by generalizing [NP22] and…
In real networks complex topological features are often associated with a diversity of interactions as measured by the weights of the links. Moreover, spatial constraints may as well play an important role, resulting in a complex interplay…
Within the context of stochastic probing with commitment, we consider the online stochastic matching problem; that is, the one sided online bipartite matching problem where edges adjacent to an online node must be probed to determine if…
Dense networks with weighted connections often exhibit a community like structure, where although most nodes are connected to each other, different patterns of edge weights may emerge depending on each node's community membership. We…
Vertex integrity is a graph parameter that measures the connectivity of a graph. Informally, its meaning is that a graph has small vertex integrity if it has a small separator whose removal disconnects the graph into connected components…
Reconfigurable optical topologies are emerging as a promising technology to improve the efficiency of datacenter networks. This paper considers the problem of scheduling opportunistic links in such reconfigurable datacenters. We study the…
Data augmentation is practically helpful for visual recognition, especially at the time of data scarcity. However, such success is only limited to quite a few light augmentations (e.g., random crop, flip). Heavy augmentations are either…
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…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
We consider the multiple traveling salesman problem on a weighted tree. In this problem there are $m$ salesmen located at the root initially. Each of them will visit a subset of vertices and return to the root. The goal is to assign a tour…