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View article: A Faster Randomized Algorithm for Vertex Cover: An Automated Approach
A Faster Randomized Algorithm for Vertex Cover: An Automated Approach Open
This work introduces two techniques for the design and analysis of branching algorithms, illustrated through the case study of the Vertex Cover problem. First, we present a method for automatically generating branching rules through a syst…
View article: A Piecewise Approach for the Analysis of Exact Algorithms
A Piecewise Approach for the Analysis of Exact Algorithms Open
To analyze the worst-case running time of branching algorithms, the majority of work in exponential time algorithms focuses on designing complicated branching rules over developing better analysis methods for simple algorithms. In the mid-…
View article: Quantum Algorithms for Graph Coloring and other Partitioning, Covering, and Packing Problems
Quantum Algorithms for Graph Coloring and other Partitioning, Covering, and Packing Problems Open
Let U be a universe on n elements, let k be a positive integer, and let F be a family of (implicitly defined) subsets of U. We consider the problems of partitioning U into k sets from F, covering U with k sets from F, and packing k non-int…
View article: Faster Algorithms for Weak Backdoors
Faster Algorithms for Weak Backdoors Open
A weak backdoor, or simply a backdoor, for a Boolean SAT formula F into a class of SAT formulae C is a partial truth assignment T such that F[T] is in C and satisfiability is preserved. The problem of finding a backdoor from class C1 into …
View article: Making the Most of Parallel Composition in Differential Privacy
Making the Most of Parallel Composition in Differential Privacy Open
We show that the ‘optimal’ use of the parallel composition theorem corresponds to finding the size of the largest subset of queries that ‘overlap’ on the data domain, a quantity we call the maximum overlap of the queries. It has previously…
View article: Making the Most of Parallel Composition in Differential Privacy
Making the Most of Parallel Composition in Differential Privacy Open
We show that the ‘optimal’ use of the parallel composition theorem corresponds to finding the size of the largest subset of queries that ‘overlap’ on the data domain, a quantity we call the maximum overlap of the queries. It has previously…
View article: Don't Be Strict in Local Search!
Don't Be Strict in Local Search! Open
Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k-exchange neighborhood. This is the set of solutions that can be obta…
View article: On Finding Optimal Polytrees
On Finding Optimal Polytrees Open
Inferring probabilistic networks from data is a notoriously difficult task. Under various goodness-of-fit measures, finding an optimal network is NP-hard, even if restricted to polytrees of bounded in-degree. Polynomial-time algorithms are…
View article: Mechanism Design for School Choice with Soft Diversity Constraints
Mechanism Design for School Choice with Soft Diversity Constraints Open
We study the controlled school choice problem where students may belong to overlapping types and schools have soft target quotas for each type. We formalize fairness concepts for the setting that extend fairness concepts considered for res…
View article: From Matching with Diversity Constraints to Matching with Regional Quotas
From Matching with Diversity Constraints to Matching with Regional Quotas Open
In the past few years, several new matching models have been proposed and studied that take into account complex distributional constraints. Relevant lines of work include (1) school choice with diversity constraints where students have (p…
View article: Fair Online Allocation of Perishable Goods and its Application to Electric Vehicle Charging
Fair Online Allocation of Perishable Goods and its Application to Electric Vehicle Charging Open
We consider mechanisms for the online allocation of perishable resources such as energy or computational power. A main application is electric vehicle charging where agents arrive and leave over time. Unlike previous work, we consider mech…
View article: Optimal Surveillance of Covert Networks by Minimizing Inverse Geodesic Length
Optimal Surveillance of Covert Networks by Minimizing Inverse Geodesic Length Open
The inverse geodesic length (IGL) is a well-known and widely used measure of network performance. It equals the sum of the inverse distances of all pairs of vertices. In network analysis, IGL of a network is often used to assess and evalua…
View article: Minimizing and Computing the Inverse Geodesic Length on Trees
Minimizing and Computing the Inverse Geodesic Length on Trees Open
For any fixed measure H that maps graphs to real numbers, the MinH problem is defined as follows: given a graph G, an integer k, and a target tau, is there a set S of k vertices that can be deleted, so that H(G - S) is at most tau? In this…
View article: Enumeration of Preferred Extensions in Almost Oriented Digraphs
Enumeration of Preferred Extensions in Almost Oriented Digraphs Open
In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on n vertices, all pre…
View article: From matching with diversity constraints to matching with regional quotas
From matching with diversity constraints to matching with regional quotas Open
In the past few years, several new matching models have been proposed and studied that take into account complex distributional constraints. Relevant lines of work include (1) school choice with diversity constraints where students have (p…
View article: On the Parameterized Cluster Editing with Vertex Splitting Problem.
On the Parameterized Cluster Editing with Vertex Splitting Problem. Open
In the Cluster Editing problem, a given graph is to be transformed into a disjoint union of cliques via a minimum number of edge editing operations. In this paper we introduce a new variant of Cluster Editing whereby a vertex can be divide…
View article: Dataset for "Fair Online Allocation of Perishable Goods and its Application to Electric Vehicle Charging"
Dataset for "Fair Online Allocation of Perishable Goods and its Application to Electric Vehicle Charging" Open
Data supporting the paper: E. Gerding, A. Perez-Diaz, H. Aziz, S. Gaspers, A. Marcu, N. Mattei, T. Walsh. "Fair Online Allocation of Perishable Goods and its Application to Electric Vehicle Charging", Proceedings of the 28th International …
View article: Cluster Editing with Vertex Splitting
Cluster Editing with Vertex Splitting Open
Cluster Editing, also known as Correlation Clustering, is a well-studied graph modification problem. In this problem, one is given a graph and the task is to perform up to $k$ edge additions or deletions to transform it into a cluster grap…
View article: Minimizing and Computing the Inverse Geodesic Length on Trees
Minimizing and Computing the Inverse Geodesic Length on Trees Open
For any fixed measure $H$ that maps graphs to real numbers, the MinH problem is defined as follows: given a graph $G$, an integer $k$, and a target $τ$, is there a set $S$ of $k$ vertices that can be deleted, so that $H(G - S)$ is at most …
View article: $(2P_2,K_4)$-Free Graphs are 4-Colorable
$(2P_2,K_4)$-Free Graphs are 4-Colorable Open
In this paper, we show that every $(2P_2,K_4)$-free graph is 4-colorable. The bound is attained by the five-wheel and the complement of the seven-cycle. This answers an open question by Wagon \cite{Wa80} in the 1980s. Our result can also b…
View article: Minesweeper with Limited Moves
Minesweeper with Limited Moves Open
We consider the problem of playing Minesweeper with a limited number of moves: Given a partially revealed board, a number of available clicks k, and a target probability p, can we win with probability p. We win if we do not click on a mine…
View article: Colouring Square-Free Graphs without Long Induced Paths
Colouring Square-Free Graphs without Long Induced Paths Open
The Colouring problem is to decide if the vertices of a graph can be coloured with at most k colours for a given integer k such that no two adjacent vertices are coloured alike. The complexity of Colouring is fully understood for graph cla…
View article: Barrier Coverage with Non-uniform Lengths to Minimize Aggregate Movements
Barrier Coverage with Non-uniform Lengths to Minimize Aggregate Movements Open
Given a line segment $I=[0,L]$, the so-called barrier, and a set of $n$ sensors with varying ranges positioned on the line containing $I$, the barrier coverage problem is to move the sensors so that they cover $I$, while minimising the tot…