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Iterative rounding and relaxation have arguably become the method of choice in dealing with unconstrained and constrained network design problems. In this paper we extend the scope of the iterative relaxation method in two directions: (1)…
We study the network pricing problem where the leader maximizes their revenue by determining the optimal amounts of tolls to charge on a set of arcs, under the assumption that the followers will react rationally and choose the shortest…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
A branch vertex in a tree is a vertex of degree at least three. We prove that, for all $s\geq 1$, every connected graph on $n$ vertices with minimum degree at least $(\frac{1}{s+3}+o(1))n$ contains a spanning tree having at most $s$ branch…
Designing well-connected graphs is a fundamental problem that frequently arises in various contexts across science and engineering. The weighted number of spanning trees, as a connectivity measure, emerges in numerous problems and plays a…
Overparameterization and overfitting are common concerns when designing and training deep neural networks, that are often counteracted by pruning and regularization strategies. However, these strategies remain secondary to most learning…
We consider the multiple unicast problem under network coding over directed acyclic networks when there are two source-terminal pairs, $s_1-t_1$ and $s_2-t_2$. Current characterizations of the multiple unicast capacity region in this…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
We introduce a tree-based formulation for the minimum-cost multi-commodity flow problem that addresses large-scale instances. The method decomposes the source-based model by representing flows as convex combinations of trees rooted at…
This paper deals with the multiobjective version of the optimal spanning tree problem. More precisely, we are interested in determining the optimal spanning tree according to an Ordered Weighted Average (OWA) of its objective values. We…
We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e. packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We…
We study the minimum diameter spanning tree problem under the reload cost model (DIAMETER-TREE for short) introduced by Wirth and Steffan (2001). In this problem, given an undirected edge-colored graph $G$, reload costs on a path arise at a…
We study the crossing-minimization problem in a layered graph drawing of planar-embedded rooted trees whose leaves have a given total order on the first layer, which adheres to the embedding of each individual tree. The task is then to…
The shortest path problem in graphs is a cornerstone of AI theory and applications. Existing algorithms generally ignore edge weight computation time. We present a generalized framework for weighted directed graphs, where edge weight can be…
Several novel mixed-integer linear and bilinear formulations are proposed for the optimum communication spanning tree problem. They implement the distance-based approach: graph distances are directly modeled by continuous, integral, or…
The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…
Disentangling two or more cables requires many steps to remove crossings between and within cables. We formalize the problem of disentangling multiple cables and present an algorithm, Iterative Reduction Of Non-planar Multiple cAble kNots…
The minimum spanning tree of a graph is a well-studied structure that is the basis of countless graph theoretic and optimization problem. We study the minimum spanning tree (MST) perturbation problem where the goal is to spend a fixed…
We are interested in the design of robust (or resilient) capacitated rooted Steiner networks in case of terminals with uniform demands. Formally, we are given a graph, capacity and cost functions on the edges, a root, a subset of nodes…
We study budget constrained network upgradeable problems. We are given an undirected edge weighted graph $G=(V,E)$ where the weight an edge $e \in E$ can be upgraded for a cost $c(e)$. Given a budget $B$ for improvement, the goal is to find…