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This paper focuses on finding a spanning tree of a graph to maximize the number of its internal vertices. We present an approximation algorithm for this problem which can achieve a performance ratio $\frac{4}{3}$ on undirected simple…
We study a number of multi-route cut problems: given a graph G=(V,E) and connectivity thresholds k_(u,v) on pairs of nodes, the goal is to find a minimum cost set of edges or vertices the removal of which reduces the connectivity between…
Operators of networks covering large areas are confronted with demands from some of their customers who are virtual service providers. These providers may call for the connectivity service which fulfils the specificity of their services,…
We study the problem of exploring all vertices of an undirected weighted graph that is initially unknown to the searcher. An edge of the graph is only revealed when the searcher visits one of its endpoints. Beginning at some start node, the…
Consider a network design application where we wish to lay down a minimum-cost spanning tree in a given graph; however, we only have stochastic information about the edge costs. To learn the precise cost of any edge, we have to conduct a…
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…
Finding optimal paths in connected graphs requires determining the smallest total cost for traveling along the graph's edges. This problem can be solved by several classical algorithms where, usually, costs are predefined for all edges.…
We consider the following general network design problem on directed graphs. The input is an asymmetric metric $(V,c)$, root $r^{*}\in V$, monotone submodular function $f:2^V\rightarrow \mathbb{R}_+$ and budget $B$. The goal is to find an…
Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al. [PODC'03] is the network creation game, where agents correspond to nodes in a network which…
We present pricing mechanisms for several online resource allocation problems which obtain tight or nearly tight approximations to social welfare. In our settings, buyers arrive online and purchase bundles of items; buyers' values for the…
We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $<u, v>$, along with a…
We consider the problem of constructing a single spanning tree for the single-source buy-at-bulk network design problem for doubling-dimension graphs. We compute a spanning tree to route a set of demands (or data) along a graph to or from a…
Stochastic matching is the stochastic version of the well-known matching problem, which consists in maximizing the rewards of a matching under a set of probability distributions associated with the nodes and edges. In most stochastic…
A cut of a graph can be represented in many different ways. Here we propose to represent a cut through a ``relation tree'', which is a spanning tree with signed edges. We show that this picture helps to classify the main greedy heuristics…
When a store sells items to customers, the store wishes to determine the prices of the items to maximize its profit. Intuitively, if the store sells the items with low (resp. high) prices, the customers buy more (resp. less) items, which…
Edge Computing (EC) offers a superior user experience by positioning cloud resources in close proximity to end users. The challenge of allocating edge resources efficiently while maximizing profit for the EC platform remains a sophisticated…
A cactus graph is a graph in which any two cycles are edge-disjoint. We present a constructive proof of the fact that any plane graph $G$ contains a cactus subgraph $C$ where $C$ contains at least a $\frac{1}{6}$ fraction of the triangular…
The evolution of smart microgrid and its demand-response characteristics not only will change the paradigms of the century-old electric grid but also will shape the electricity market. In this new market scenario, once always energy…
Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…
The inefficiency of the Wardrop equilibrium of nonatomic routing games can be eliminated by placing tolls on the edges of a network so that the socially optimal flow is induced as an equilibrium flow. A solution where the minimum number of…