Related papers: Burning graphs through farthest-first traversal
This paper discusses the shortest path problem in a general directed graph with $n$ nodes and $K$ cost scenarios (objectives). In order to choose a solution, the min-max criterion is applied. The min-max version of the problem is hard to…
The graph Fourier transform (GFT) is in general dense and requires O(n^2) time to compute and O(n^2) memory space to store. In this paper, we pursue our previous work on the approximate fast graph Fourier transform (FGFT). The FGFT is…
One of the most important combinatorial optimization problems is graph coloring. There are several variations of this problem involving additional constraints either on vertices or edges. They constitute models for real applications, such…
We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, including the (conditional) graph entropy, rate-distortion functions and…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
A common way of partitioning graphs is through minimum cuts. One drawback of classical minimum cut methods is that they tend to produce small groups, which is why more balanced variants such as normalized and ratio cuts have seen more…
Combinatorial optimization is a fundamental problem found in many fields. In many real life situations, the constraints and the objective function forming the optimization problem are naturally distributed amongst different sites in some…
The Correlation Clustering problem is one of the most extensively studied clustering formulations due to its wide applications in machine learning, data mining, computational biology and other areas. We consider the Correlation Clustering…
The Firefighter problem and a variant of it, known as Resource Minimization for Fire Containment (RMFC), are natural models for optimal inhibition of harmful spreading processes. Despite considerable progress on several fronts, the…
The problem of finding an optimal vertex cover in a graph is a classic NP-complete problem, and is a special case of the hitting set question. On the other hand, the hitting set problem, when asked in the context of induced geometric…
In the restricted shortest paths problem, we are given a graph $G$ whose edges are assigned two non-negative weights: lengths and delays, a source $s$, and a delay threshold $D$. The goal is to find, for each target $t$, the length of the…
Consider a model of fire spreading through a graph; initially some vertices are burning, and at every given time-step fire spreads from burning vertices to their neighbours. The firefighter problem is a solitaire game in which a player is…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
Analyzing large graph data is an essential part of many modern applications, such as social networks. Due to its large computational complexity, distributed processing is frequently employed. This requires graph data to be divided across…
We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…
Graph-based algorithms have demonstrated state-of-the-art performance in the nearest neighbor search (NN-Search) problem. These empirical successes urge the need for theoretical results that guarantee the search quality and efficiency of…
We consider the communication complexity of finding an approximate maximum matching in a graph in a multi-party message-passing communication model. The maximum matching problem is one of the most fundamental graph combinatorial problems,…
Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…
We investigate a fundamental vertex-deletion problem called (Induced) Subgraph Hitting: given a graph $G$ and a set $\mathcal{F}$ of forbidden graphs, the goal is to compute a minimum-sized set $S$ of vertices of $G$ such that $G-S$ does…
We consider a variation of the prototype combinatorial-optimisation problem known as graph-colouring. Our optimisation goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximise the number of different…