Approximating the graph diameter is a basic task of both theoretical and practical interest. A simple folklore algorithm can output a 2-approximation to the diameter in linear time by running BFS from an arbitrary vertex. It has been open whether a better ...

We consider the following well-studied problem of metric distortion in social choice. Suppose that we have an election with n voters and m candidates located in a shared metric space. We would like to design a voting rule that chooses a candidate whose ...

We present dynamic algorithms with polylogarithmic update time for estimating the size of the maximum matching of a graph undergoing edge insertions and deletions with approximation ratio strictly better than 2. Specifically, we obtain a \(\(1+\tfrac{1}{\...\)

A constraint satisfaction problem (CSP), \(\textsf {Max-CSP}(\mathcal {F})\), is specified by a finite set of constraints \(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\) for positive integers q and k. An instance of the ...

We consider the numerical taxonomy problem of fitting a positive distance function \({\mathcal {D}:{S\choose 2}\rightarrow \mathbb {R}_{\gt 0}}\) by a tree metric. We want a tree T with positive edge weights and including S among the vertices so that ...

We identify a sufficient condition, treewidth-pliability, that gives a polynomial-time algorithm for an arbitrarily good approximation of the optimal value in a large class of Max-2-CSPs parameterised by the class of allowed constraint graphs (with ...

There has been a long history of studying randomized greedy matching algorithms since the work by Dyer and Frieze [9]. We follow this trend and consider the problem formulated in the oblivious setting, in which the vertex set of a graph is known to the ...

We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multiplayer model ...

We show that for any finite point set P in the plane and ϵ > 0 there exist \( O(\tfrac{1}{{\epsilon }^{3/2+\gamma }}) \) points in ℝ², for arbitrary small γ > 0, that pierce every convex set K with |K∩ P|> ϵ |P|. This is the first improvement of the ...

In this article, we consider the following question: Can we optimize objective functions from the training data we use to learn them? We formalize this question through a novel framework we call optimization from samples (OPS). In OPS, we are given ...

We consider the classic Facility Location, k-Median, and k-Means problems in metric spaces of doubling dimension d. We give nearly linear-time approximation schemes for each problem. The complexity of our algorithms is Õ(2^(1/ε)O(d2) n), making a ...

The edit distance between two strings is defined as the smallest number of insertions, deletions, and substitutions that need to be made to transform one of the strings to another one. Approximating edit distance in subquadratic time is “one of the ...

We give a constant-factor approximation algorithm for the asymmetric traveling salesman problem (ATSP). Our approximation guarantee is analyzed with respect to the standard LP relaxation, and thus our result confirms the conjectured constant integrality ...

Edit distance is a measure of similarity of two strings based on the minimum number of character insertions, deletions, and substitutions required to transform one string into the other. The edit distance can be computed exactly using a dynamic ...

In a generalized network design (GND) problem, a set of resources are assigned (non-exclusively) to multiple requests. Each request contributes its weight to the resources it uses and the total load on a resource is then translated to the cost it incurs ...

Hierarchical clustering is a recursive partitioning of a dataset into clusters at an increasingly finer granularity. Motivated by the fact that most work on hierarchical clustering was based on providing algorithms, rather than optimizing a specific ...

A metric tree embedding of expected stretch α ≥ 1 maps a weighted n-node graph G = (V, E, ω) to a weighted tree T = (V_T, E_T , ω_T) with V ⊑ V_T such that, for all v,w ∈ V, dist(v, w, G) ≤ dist(v, w, T), and E[dist(v, w, T)] ≤ α dist(v, w, G). Such ...

We introduce and study a general scheduling problem that we term the Polytope Scheduling problem (PSP). In this problem, jobs can have different arrival times and sizes, and the rates assigned by the scheduler to the jobs are subject to arbitrary ...

We initiate a study of learning and testing dynamic environments, focusing on environments that evolve according to a fixed local rule. The (proper) learning task consists of obtaining the initial configuration of the environment, whereas for nonproper ...

We present a simple deterministic distributed (2 + ϵ)-approximation algorithm for minimum-weight vertex cover, which completes in O(log Δ/ϵlog log Δ) rounds, where Δ is the maximum degree in the graph, for any ϵ > 0 that is at most O(1). For a constant ...