ACM Transactions on Algorithms

We study the k-route cut problem: given an undirected edge-weighted graph G = (V, E), a collection {(s₁, t₁), (s₂, t₂), …, (s_r, t_r)} of source-sink pairs, and an integer connectivity requirement k, the goal is to find a minimum-weight subset E′ of edges ...

We consider the problem of computing the distance between two piecewise-linear bivariate functions f and g defined over a common domain M, induced by the L₂ norm—that is, ‖ f - g‖2 = √∫_M(f - g)². If f is defined by linear interpolation over a ...

We investigate fast algorithms for changing between the standard basis and an orthogonal basis of idempotents for Möbius algebras of finite lattices. We show that every lattice with v elements, n of which are nonzero and join-irreducible (or, by a dual ...

In this article, we show how to compute the width of a dynamic set of low-dimensional points in the streaming model. In particular, we assume that the stream contains both insertions of points and deletions of points to a set S, and the goal is to ...

The Unique Games Conjecture (UGC) has emerged in recent years as the starting point for several optimal inapproximability results. While for none of these results a reverse reduction to Unique Games is known, the assumption of bijective projections in ...

A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) n-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that outperforms the naïve O(...

We show that linear probing requires 5-independent hash functions for expected constant-time performance, matching an upper bound of Pagh et al. [2009]. More precisely, we construct a random 4-independent hash function yielding expected logarithmic ...

Many fast graph algorithms begin by preprocessing the graph to improve its sparsity. A common form of this is spectral sparsification, which involves removing and reweighting the edges of the graph while approximately preserving its spectral properties. ...

Consider the following problem: given a set system (U, Ω) and an edge-weighted graph G = (U, E) on the same universe U, find the set A ∈ Ω such that the Steiner tree cost with terminals A is as large as possible—“which set in Ω is the most difficult to ...

How does one verify that the output of a complicated program is correct? One can formally prove that the program is correct, but this may be beyond the power of existing methods. Alternatively, one can check that the output produced for a particular ...

We present a (1 + ε)-approximation algorithm running in O(f(ε) · nlog ⁴n) time for finding the diameter of an undirected planar graph with n vertices and with nonnegative edge lengths.