Removing and Adding Edges for the Traveling Salesman Problem

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Given a source of iid samples of edges of an input graph G with n vertices and m edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in G? Moreover, is it possible to obtain such an estimate in a sm ...

In this thesis, we give new approximation algorithms for some NP-hard problems arising in resource allocation and network design. As a resource allocation problem, we study the Santa Claus problem (also known as the MaxMin Fair Allocation problem) in which ...

Several discrete geometry problems are equivalent to estimating the size of the largest homogeneous sets in graphs that happen to be the union of few comparability graphs. An important observation for such results is that if G is an n-vertex graph that is ...

Let G be a drawing of a graph with n vertices and e > 4n edges, in which no two adjacent edges cross and any pair of independent edges cross at most once. According to the celebrated Crossing Lemma of Ajtai, Chvatal, Newborn, Szemeredi and Leighton, the nu ...

Graph comparison deals with identifying similarities and dissimilarities between graphs. A major obstacle is the unknown alignment of graphs, as well as the lack of accurate and inexpensive comparison metrics. In this work we introduce the filter graph dis ...

This paper is devoted to the distributed complexity of finding an approximation of the maximum cut (MAXCUT) in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any communica ...

An integer program (IP) is a problem of the form

\min \{f(x) : \, Ax = b, \ l \leq x \leq u, \ x \in \Z^n\}

, where

A \in \Z^{m \times n}

b \in \Z^m

l,u \in \Z^n

, and

f: \Z^n \rightarrow \Z

is a separable convex objective function. The problem o ...

Consider the family of bounded degree graphs in any minor-closed family (such as planar graphs). Let d be the degree bound and n be the number of vertices of such a graph. Graphs in these classes have hyperfinite decompositions, where, one removes a small ...

In this note, we improve on results of Hoppen, Kohayakawa and Lefmann about the maximum number of edge colorings without monochromatic copies of a star of a fixed size that a graph on n vertices may admit. Our results rely on an improved application of an ...

We study experiment design for unique identification of the causal graph of a system where the graph may contain cycles. The presence of cycles in the structure introduces major challenges for experiment design as, unlike acyclic graphs, learning the skele ...

We study in this thesis the asymptotic behavior of optimal paths on a random graph model, the configuration model, for which we assign continuous random positive weights on its edges. We start by describing the asymptotic behavior of the diameter and the f ...

We consider the problem of learning implicit neural representations (INRs) for signals on non-Euclidean domains. In the Euclidean case, INRs are trained on a discrete sampling of a signal over a regular lattice. Here, we assume that the continuous signal e ...

The min knapsack problem appears as a major component in the structure of capacitated covering problems. Its polyhedral relaxations have been extensively studied, leading to strong relaxations for networking, scheduling and facility location problems. ...

The metric dimension (MD) of a graph is a combinatorial notion capturing the minimum number of landmark nodes needed to distinguish every pair of nodes in the graph based on graph distance. We study how much the MD can increase if we add a single edge to t ...

We study different symbolic algorithms to solve two related reconfiguration problems on graphs: the token swapping problem and the permutation routing via matchings problem. Input to both problems is a connected graph with labeled vertices and a token in e ...

Removing and Adding Edges for the Traveling Salesman Problem

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Space Efficient Approximation to Maximum Matching Size from Uniform Edge Samples

Approximation Algorithms for Allocation and Network Design

Improved Ramsey-type results for comparability graphs

A Crossing Lemma for Multigraphs

fGOT: Graph Distances Based on Filters and Optimal Transport

Local approximation of the Maximum Cut in regular graphs

New Results in Integer and Lattice Programming

Random walks and forbidden minors III: poly(d epsilon(-1))-time partition oracles for minor-free graph classes

Edge colorings of graphs without monochromatic stars

A Unified Experiment Design Approach for Cyclic and Acyclic Causal Models

Non-Exponential Variations for Classical Results in First Passage Percolation

Generalised Implicit Neural Representations

On inequalities with bounded coefficients and pitch for the min knapsack polytope

On the robustness of the metric dimension of grid graphs to adding a single edge

Symbolic Algorithms for Token Swapping