Related papers: Optimal Extended Formulations from Optimal Dynamic…
We initiate the theoretical study of Ext-TSP, a problem that originates in the area of profile-guided binary optimization. Given a graph $G=(V, E)$ with positive edge weights $w: E \rightarrow R^+$, and a non-increasing discount function…
The Virtual Network Embedding Problem (VNEP) considers the efficient allocation of resources distributed in a substrate network to a set of request networks. Many existing works discuss either heuristics or exact algorithms, resulting in a…
A perfect matching in an undirected graph $G=(V,E)$ is a set of vertex disjoint edges from $E$ that include all vertices in $V$. The perfect matching problem is to decide if $G$ has such a matching. Recently Rothvo{\ss} proved the striking…
The question if a given partial solution to a problem can be extended reasonably occurs in many algorithmic approaches for optimization problems. For instance, when enumerating minimal dominating sets of a graph $G=(V,E)$, one usually…
This thesis explores algorithmic applications and limitations of convex relaxation hierarchies for approximating some discrete and continuous optimization problems. - We show a dichotomy of approximability of constraint satisfaction…
We consider extension variants of the classical graph problems Vertex Cover and Independent Set. Given a graph $G=(V,E)$ and a vertex set $U \subseteq V$, it is asked if there exists a minimal vertex cover (resp.\ maximal independent set)…
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…
The phylogenetic tree construction is to infer the evolutionary relationship between species from the experimental data. However, the experimental data are often imperfect and conflicting each others. Therefore, it is important to extract…
There has been recent progress in showing that the exponential dependence on treewidth in dynamic programming algorithms for solving NP-hard problems are optimal under the Strong Exponential Time Hypothesis (SETH). We extend this work to…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
In the \textsc{Maximum Degree Contraction} problem, input is a graph $G$ on $n$ vertices, and integers $k, d$, and the objective is to check whether $G$ can be transformed into a graph of maximum degree at most $d$, using at most $k$ edge…
In the Partial Vertex Cover (PVC) problem, we are given an $n$-vertex graph $G$ and a positive integer $k$, and the objective is to find a vertex subset $S$ of size $k$ maximizing the number of edges with at least one end-point in $S$. This…
We introduce a method for proving lower bounds on the efficacy of semidefinite programming (SDP) relaxations for combinatorial problems. In particular, we show that the cut, TSP, and stable set polytopes on $n$-vertex graphs are not the…
A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…
A popular method in combinatorial optimization is to express polytopes P, which may potentially have exponentially many facets, as solutions of linear programs that use few extra variables to reduce the number of constraints down to a…
Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical…
There has been considerable recent interest in computing a diverse collection of solutions to a given optimization problem, both in the AI and theory communities. Given a classical optimization problem $\Pi$ (e.g., spanning tree, minimum…
Semidefinite programs (SDPs) are standard convex problems that are frequently found in control and optimization applications. Interior-point methods can solve SDPs in polynomial time up to arbitrary accuracy, but scale poorly as the size of…
Densest Subgraph Problem (DSP) is an important primitive problem with a wide range of applications, including fraud detection, community detection and DNA motif discovery. Edge-based density is one of the most common metrics in DSP.…
In this work we design graph neural network architectures that capture optimal approximation algorithms for a large class of combinatorial optimization problems, using powerful algorithmic tools from semidefinite programming (SDP).…