Note: When clicking on a Digital Object Identifier (DOI) number, you will be taken to an external site maintained by the publisher.
Some full text articles may not yet be available without a charge during the embargo (administrative interval).
What is a DOI Number?
Some links on this page may take you to nonfederal websites. Their policies may differ from this site.

Free, publiclyaccessible full text available February 1, 2023

Free, publiclyaccessible full text available January 1, 2023

Free, publiclyaccessible full text available January 1, 2023

Free, publiclyaccessible full text available January 1, 2023

Free, publiclyaccessible full text available January 1, 2023

The problem of sparsifying a graph or a hypergraph while approximately preserving its cut structure has been extensively studied and has many applications. In a seminal work, Benczúr and Karger (1996) showed that given any nvertex undirected weighted graph G and a parameter ε ∈ (0,1), there is a nearlinear time algorithm that outputs a weighted subgraph G' of G of size Õ(n/ε²) such that the weight of every cut in G is preserved to within a (1 ± ε)factor in G'. The graph G' is referred to as a (1 ± ε)approximate cut sparsifier of G. Subsequent recent work has obtained a similar result for the more general problem of hypergraph cut sparsifiers. However, all known sparsification algorithms require Ω(n + m) time where n denotes the number of vertices and m denotes the number of hyperedges in the hypergraph. Since m can be exponentially large in n, a natural question is if it is possible to create a hypergraph cut sparsifier in time polynomial in n, independent of the number of edges. We resolve this question in the affirmative, giving the first sublinear time algorithm for this problem, given appropriate query access to the hypergraph. Specifically, we designmore »

Vehicle routing problems are a broad class of combinatorial optimization problems that can be formulated as the problem of finding a tour in a weighted graph that optimizes some function of the visited vertices. For instance, a canonical and extensively studied vehicle routing problem is the orienteering problem where the goal is to find a tour that maximizes the number of vertices visited by a given deadline. In this paper, we consider the computational tractability of a wellknown generalization of the orienteering problem called the OrientMTW problem. The input to OrientMTW consists of a weighted graph G(V, E) where for each vertex v ∊ V we are given a set of time instants Tv ⊆ [T], and a source vertex s. A tour starting at s is said to visit a vertex v if it transits through v at any time in the set Tv. The goal is to find a tour starting at the source vertex that maximizes the number of vertices visited. It is known that this problem admits a quasipolynomial time O(log OPT)approximation ratio where OPT is the optimal solution value but until now no hardness better than an APXhardness was known for this problem. Our mainmore »