We initiate the study of the following natural geometric optimization problem. The input is a set of axis-aligned rectangles in the plane. The objective is to find a set of horizontal line segments of minimum total length so that every rectangle is stabbed by some line segment. A line segment stabs a rectangle if it intersects its left and its right boundary. The problem, which...

Deciding two-guard walkability of an n-sided polygon is a well-understood problem. We study the following more general question: How far can two guards reach from a given source vertex while staying mutually visible, in the (more realistic) case that the polygon is not entirely walkable? There can be Theta(n) such maximal walks, and we show how to find all of them in O(n log n...

Suppose we are given a set D of n pairwise intersecting disks in the plane. A planar point set P stabs D if and only if each disk in D contains at least one point from P. We present a deterministic algorithm that takes O(n) time to find five points that stab D. Furthermore, we give a simple example of 13 pairwise intersecting disks that cannot be stabbed by three points. This...

We address the following general question: given a graph class C on which we can solve Maximum Matching in (quasi) linear time, does the same hold true for the class of graphs that can be modularly decomposed into C? As a way to answer this question for distance-hereditary graphs and some other superclasses of cographs, we study the combined effect of modular decomposition with a...

We present a Monte Carlo algorithm that detects the presence of a Hamiltonian cycle in an n-vertex undirected bipartite graph of average degree delta >= 3 almost surely and with no false positives, in (2-2^{1-delta})^{n/2}poly(n) time using only polynomial space. With the exception of cubic graphs, this is faster than the best previously known algorithms. Our method is a...

We investigate the complexity of the separation problem associated to classes of regular languages. For a class C, C-separation takes two regular languages as input and asks whether there exists a third language in C which includes the first and is disjoint from the second. First, in contrast with the situation for the classical membership problem, we prove that for most classes...

Karp and Miller's algorithm is a well-known decision procedure that solves the termination and boundedness problems for vector addition systems with states (VASS), or equivalently Petri nets. This procedure was later extended to a general class of models, well-structured transition systems, and, more recently, to pushdown VASS. In this paper, we extend pushdown VASS to higher...

We introduce the Delta-framework, LF_Delta, a dependent type theory based on the Edinburgh Logical Framework LF, extended with the strong proof-functional connectives, i.e. strong intersection, minimal relevant implication and strong union. Strong proof-functional connectives take into account the shape of logical proofs, thus reflecting polymorphic features of proofs in formulae...

Given a host graph G and a pattern graph H, the induced subgraph isomorphism problem is to decide whether G contains an induced subgraph that is isomorphic to H. We study the time complexity of induced subgraph isomorphism problems when the pattern graph is fixed. Nesetril and Poljak gave an O(n^{k omega}) time algorithm that decides the induced subgraph isomorphism problem for...

Our input is a complete graph G = (V,E) on n vertices where each vertex has a strict ranking of all other vertices in G. The goal is to construct a matching in G that is "globally stable" or popular. A matching M is popular if M does not lose a head-to-head election against any matching M': here each vertex casts a vote for the matching in {M,M'} where it gets a better assignment...

In this paper, we present a probabilistic analysis of Boolean games. We consider the class of Boolean games where payoff functions are given by random Boolean formulas. This permits to study certain properties of this class in its totality, such as the probability of existence of a winning strategy, including its asymptotic behaviour. With the help of the Coq proof assistant, we...

Radio networks are a long-studied model for distributed system of devices which communicate wirelessly. When these devices are mobile or have limited capabilities, the system is best modeled by the ad-hoc variant, in which the devices do not know the structure of the network. Much work has been devoted to designing algorithms for the ad-hoc model, particularly for fundamental...

We provide the first asynchronous distributed algorithms to compute broadcast and minimum spanning tree with o(m) bits of communication, in a sufficiently dense graph with n nodes and m edges. For decades, it was believed that Omega(m) bits of communication are required for any algorithm that constructs a broadcast tree. In 2015, King, Kutten and Thorup showed that in the KT1...

We study distributed algorithms for the maximum matching problem in the CONGEST model, where each message must be bounded in size. We give new deterministic upper bounds, and a new lower bound on the problem. We begin by giving a distributed algorithm that computes an exact maximum (unweighted) matching in bipartite graphs, in O(n log n) rounds. Next, we give a distributed...

Timed automata are powerful models for the analysis of real time systems. The optimal infinite scheduling problem for double-priced timed automata is concerned with finding infinite runs of a system whose long term cost to reward ratio is minimal. Due to the state-space explosion occurring when discretising a timed automaton, exact computation of the optimal infinite ratio is...

Program synthesis constructs programs from specifications in an automated way. Strategy Logic (SL) is a powerful and versatile specification language whose goal is to give theoretical foundations for program synthesis in a multi-agent setting. One limitation of Strategy Logic is that it is purely qualitative. For instance it cannot specify quantitative properties of executions...

The central conjecture of parameterized complexity states that FPT !=W[1], and is generally regarded as the parameterized counterpart to P !=NP. We revisit the issue of the plausibility of FPT !=W[1], focusing on two aspects: the difficulty of proving the conjecture (assuming it holds), and how the relation between the two classes might differ from the one between P and NP...

We apply average-case complexity theory to physical problems modeled by continuous-time dynamical systems. The computational complexity when simulating such systems for a bounded time-frame mainly stems from trajectories coming close to complex singularities of the system. We show that if for most initial values the trajectories do not come close to singularities the simulation...

In this paper we explore hitting distributions, a notion that arose recently in the context of deterministic "query-to-communication" simulation theorems. We show that any expander in which any two distinct vertices have at most one common neighbor can be transformed into a gadget possessing good hitting distributions. We demonstrate that this result is applicable to affine plane...

In recent years, two-player zero-sum games with multiple objectives have received a lot of interest as a model for the synthesis of complex reactive systems. In this framework, Player 1 wins if he can ensure that all objectives are satisfied against any behavior of Player 2. When this is not possible to satisfy all the objectives at once, an alternative is to use some preorder on...

We study selective monitors for labelled Markov chains. Monitors observe the outputs that are generated by a Markov chain during its run, with the goal of identifying runs as correct or faulty. A monitor is selective if it skips observations in order to reduce monitoring overhead. We are interested in monitors that minimize the expected number of observations. We establish an...

Given a hypergraph H=(X,S), a planar support for H is a planar graph G with vertex set X, such that for each hyperedge S in S, the sub-graph of G induced by the vertices in S is connected. Planar supports for hypergraphs have found several algorithmic applications, including several packing and covering problems, hypergraph coloring, and in hypergraph visualization. The main...

We present two stable mergesort variants, "peeksort" and "powersort", that exploit existing runs and find nearly-optimal merging orders with negligible overhead. Previous methods either require substantial effort for determining the merging order (Takaoka 2009; Barbay & Navarro 2013) or do not have an optimal worst-case guarantee (Peters 2002; Auger, Nicaud & Pivoteau 2015; Buss...

Network analysis defines a number of centrality measures to identify the most central nodes in a network. Fast computation of those measures is a major challenge in algorithmic network analysis. Aside from closeness and betweenness, Katz centrality is one of the established centrality measures. In this paper, we consider the problem of computing rankings for Katz centrality. In...

Given a graph G and a set of terminals T, a distance emulator of G is another graph H (not necessarily a subgraph of G) containing T, such that all the pairwise distances in G between vertices of T are preserved in H. An important open question is to find the smallest possible distance emulator. We prove that, given any subset of k terminals in an n-vertex undirected unweighted...