In the trajectory segmentation problem we are given a polygonal trajectory with n vertices that we have to subdivide into a minimum number of disjoint segments (subtrajectories) that all satisfy a given criterion. The problem is known to be solvable ...

The classical problem of efficiently listing all the simple cycles in a graph has been studied since the early 70s. For a graph with n vertices and m edges, containing η cycles, the most efficient solution was presented by Johnson [SIAM J. Computing, ...

Much of social network analysis is --- implicitly or explicitly --- predicated on the assumption that individuals tend to be more similar to their friends than to strangers. Thus, an observed social network provides a noisy signal about the latent ...

The triplet and quartet distances are distance measures to compare two rooted and two unrooted trees, respectively. The leaves of the two trees should have the same set of n labels. The distances are defined by enumerating all subsets of three labels (...

A consensus tree is a single phylogenetic tree that summarizes the branching structure in a given set of conflicting phylogenetic trees. Many different types of consensus trees have been proposed in the literature; three of the most well-known and ...

Given a large edge-weighted network G with k terminal vertices, we wish to compress it and store, using little memory, the value of the minimum cut (or equivalently, maximum flow) between every bipartition of terminals. One appealing methodology to ...

We consider the Euclidean facility location problem with uniform opening cost. In this problem, we are given a set of n points P ⊆ @@@@² and an opening cost f ε @@@@⁺, and we want to find a set of facilities F ⊆ @@@@² that minimizes

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where d(p, q) ...

Approximating the length of the longest increasing sequence (LIS) of an array is a well-studied problem. We study this problem in the data stream model, where the algorithm is allowed to make a single left-to-right pass through the array and the key ...

In 1944, Cairns proved the following theorem: given any two straight-line planar drawings of a triangulation with the same outer face, there exists a morph (i.e., a continuous transformation) between the two drawings so that the drawing remains straight-...

We study the worst case error of kernel density estimates via subset approximation. A kernel density estimate of a distribution is the convolution of that distribution with a fixed kernel (e.g. Gaussian kernel). Given a subset (i.e. a point set) of the ...

We consider the mobile facility location (MFL) problem. We are given a set of facilities and clients located in a common metric space G = (V, c). The goal is to move each facility from its initial location to a destination (in V) and assign each client ...

We study a fundamental measure for wireless interference in the SINR model known as (weighted) inductive independence. This measure characterizes the effectiveness of using oblivious power --- when the power used by a transmitter only depends on the ...

There has been significant interest in the networking community on the impact of cascade effects on the diffusion of networking technology upgrades in the Internet. Thinking of the global Internet as a graph, where each node represents an economically-...

Graph product is a fundamental tool with rich applications in both graph theory and theoretical computer science. It is usually studied in the form f(G * H) where G and H are graphs, * is a graph product and f is a graph property. For example, if f is ...

This work is concerned with the proof-complexity of certifying that optimization problems do not have good solutions. Specifically we consider bounded-degree "Sum of Squares" (SOS) proofs, a powerful algebraic proof system introduced in 1999 by ...

Here, we give an algorithm for deciding if the nonnegative rank of a matrix M of dimension m X n is at most r which runs in time (nm)@@@@. This is the first exact algorithm that runs in time singly-exponential in r. This algorithm (and earlier ...

Low rank approximation is a fundamental computational primitive widely used in data analysis. In many applications the dataset that the algorithm operates on may contain sensitive information about contributing individuals (e.g. user/movie ratings in ...

We determine the exact freezing threshold, r^f, for a family of models of random boolean constraint satisfaction problems, including NAE-SAT and hypergraph 2-colouring, when the constraint size is sufficiently large. If the constraint-density of a random ...

Holant problems are a general framework to study the algorithmic complexity of counting problems. Both counting constraint satisfaction problems and graph homomorphisms are special cases. All previous results of Holant problems are over the Boolean ...

The construction of exact exponential-time algorithms for NP-complete problems has for some time been a very active research area. Unfortunately, there is a lack of general methods for studying and comparing the time complexity of algorithms for such ...