We present a pseudo-polynomial time (1 + epsilon)-approximation algorithm for computing the integral and average Fr�chet distance between two given polygonal curves T_1 and T_2. The running time is in O(zeta^{4}n^4/epsilon^2) where n is the complexity of T_1 and T_2 and zeta is the maximal ratio of the lengths of any pair of segments from T_1 and T_2. Furthermore, we give...

We consider a lower- and upper-bounded generalization of the classical facility location problem, where each facility has a capacity (upper bound) that limits the number of clients it can serve and a lower bound on the number of clients it must serve if it is opened. We develop an LP rounding framework that exploits a Voronoi diagram-based clustering approach to derive the first...

We use the control features of continuation models to interpret proofs in first-order classical theories. This interpretation is suitable for extracting algorithms from proofs of Pi^0_2 formulas. It is fundamentally different from the usual direct interpretation, which is shown to be equivalent to Friedman's trick. The main difference is that atomic formulas and natural numbers...

We present sound and complete environmental bisimilarities for a variant of Dybvig et al.'s calculus of multi-prompted delimited-control operators with dynamic prompt generation. The reasoning principles that we obtain generalize and advance the existing techniques for establishing program equivalence in calculi with single-prompted delimited control. The basic theory that we...

We describe experiments in teaching fundamental informatics notions around mathematical structures for formal concepts, and effective algorithms to manipulate them. The major themes of lambda-calculus and type theory served as guides for the effective implementation of functional programming languages and higher-order proof assistants, appropriate for reflecting the theoretical...

Snake and Nibbler are two well-known video games in which a snake slithers through a maze and grows as it collects food. During this process, the snake must avoid any collision with its tail. Various goals can be associated with these video games, such as avoiding the tail as long as possible, or collecting a certain amount of food, or reaching some target location. Unfortunately...

We study streaming algorithms for partitioning integer sequences and trees. In the case of trees, we suppose that the input tree is provided by a stream consisting of a depth-first-traversal of the input tree. This captures the problem of partitioning XML streams, among other problems. We show that both problems admit deterministic (1+epsilon)-approximation streaming algorithms...

Given m distributed data streams A_1,..., A_m, we consider the problem of estimating the number of unique identifiers in streams defined by set expressions over A_1,..., A_m. We identify a broad class of algorithms for solving this problem, and show that the estimators output by any algorithm in this class are perfectly unbiased and satisfy strong variance bounds. Our analysis...

Top-k queries have become extremely popular in the database community. Such a query, which is issued on a set of elements each carrying a real-valued weight, returns the k elements with the highest weights among all the elements that satisfy a predicate. As usual, an index structure is necessary to answer a query substantially faster than accessing the whole input set. The...

We formalize and analyze a new automata-theoretic problem termed control improvisation. Given an automaton, the problem is to produce an improviser, a probabilistic algorithm that randomly generates words in its language, subject to two additional constraints: the satisfaction of an admissibility predicate, and the exhibition of a specified amount of randomness. Control...

Vertex Cover is one of the most well studied problems in the realm of parameterized algorithms and admits a kernel with O(l^2) edges and 2*l vertices. Here, l denotes the size of a vertex cover we are seeking for. A natural question is whether Vertex Cover admits a polynomial kernel (or a parameterized algorithm) with respect to a parameter k, that is, provably smaller than the...

In the Steiner Tree problem one is given an undirected graph, a subset T of its vertices, and an integer k and the question is whether there is a connected subgraph of the given graph containing all the vertices of T and at most k other vertices. The vertices in the subset T are called terminals and the other vertices are called Steiner vertices. Recently, Pilipczuk, Pilipczuk...

We study how generic is the property of nonlocality among the set of quantum correlations for bipartite dichotomic measurements. To do so, we consider the characterization of these quantum correlations as those of the form gamma = ( < u_i , v_j > )_{i,j=1}^n , where the vectors u_i and v_j are in the unit sphere of a real Hilbert space. The important parameters in this...

We propose a generalization of higher-dimensional automata, partial HDA. Unlike HDA, and also extending event structures and Petri nets, partial HDA can model phenomena such as priorities or the disabling of an event by another event. Using open maps and unfoldings, we introduce a natural notion of (higher-dimensional) bisimilarity for partial HDA and relate it to history...

For predual categories C and D we establish isomorphisms between opfibrations representing local varieties of languages in C, local pseudovarieties of D-monoids, and finitely generated profinite D-monoids. The global sections of these opfibrations are shown to correspond to varieties of languages in C, pseudovarieties of D-monoids, and profinite equational theories of D-monoids...

Recent decidability results on the satisfiability problem for temporal logics, in particular LTL, CTL* and ECTL*, with constraints over external structures like the integers with the order or infinite trees are surveyed in this paper.

This paper studies safety, progress, and non-zeno properties of Communicating Timed Automata (CTAs), which are timed automata (TA) extended with unbounded communication channels, and presents a procedure to build timed global specifications from systems of CTAs. We define safety and progress properties for CTAs by extending properties studied in communicating finite-state...

Compositional reasoning over probabilistic systems wrt. behavioral metric semantics requires the language operators to be uniformly continuous. We study which SOS specifications define uniformly continuous operators wrt. bisimulation metric semantics. We propose an expressive specification format that allows us to specify operators of any given modulus of continuity. Moreover, we...

In this paper, we introduce a novel rule for synthesis of reactive systems, applicable to systems made of n components which have each their own objectives. It is based on the notion of admissible strategies. We compare our novel rule with previous rules defined in the literature, and we show that contrary to the previous proposals, our rule define sets of solutions which are...

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performance, these methods are supported by a well-developed theory. Kernel methods use an implicit mapping of the input data into a high dimensional feature space defined by a kernel function, i.e., a function...

We study resistance sparsification of graphs, in which the goal is to find a sparse subgraph (with reweighted edges) that approximately preserves the effective resistances between every pair of nodes. We show that every dense regular expander admits a (1+epsilon)-resistance sparsifier of size ~O(n/epsilon), and conjecture this bound holds for all graphs on n nodes. In comparison...

Modern software development and run-time environments, such as Java and the Microsoft .NET Common Language Runtime (CLR), have adopted a declarative form of access control. Permissions are granted to code providers, and during execution, the platform verifies compatibility between the permissions required by a security-sensitive operation and those granted to the executing code...

Rewriting is a formalism widely used in computer science and mathematical logic. When using rewriting as a programming or modeling paradigm, the rewrite rules describe the transformations one wants to operate and declarative rewriting strategies are used to control their application. The operational semantics of these strategies are generally accepted and approaches for analyzing...

Traditionally, the performance of algorithms is evaluated using worst-case analysis. For a number of problems, this type of analysis gives overly pessimistic results: Worst-case inputs are rather artificial and do not occur in practical applications. In this lecture we review some alternative analysis approaches leading to more realistic and robust performance evaluations...

The Fr�chet distance is a popular and widespread distance measure for point sequences and for curves. About two years ago, Agarwal et al [SIAM J. Comput. 2014] presented a new (mildly) subquadratic algorithm for the discrete version of the problem. This spawned a flurry of activity that has led to several new algorithms and lower bounds. In this paper, we study the...