We show that for constraint satisfaction problems (CSPs), weakly exponential size linear programming relaxations are as powerful as the explicit linear program described by $n^{\Omega(1)}$-rounds of the Sherali--Adams linear programming hierarchy. ...

Explaining the excellent practical performance of the simplex method for linear programming has been a major topic of research for over 50 years. One of the most successful frameworks for understanding the simplex method was given by Spielman and Teng [J. ...

Motivated by online advertisement and exchange settings, greedy randomized algorithms for the maximum matching problem have been studied, in which the algorithm makes (random) decisions that are essentially oblivious to the input graph. Any greedy ...

Let $D$, called the domain, be a fixed finite set and let $\Gamma$, called the valued constraint language, be a fixed set of functions of the form $f:D^m\to\mathbb{Q}\cup\{\infty\}$, where different functions might have different arity $m$. We study the ...

We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset linear programming relaxation for ...

Minimum-weight triangulation (MWT) is NP-hard. It has a polynomial-time constant-factor approximation algorithm, and a variety of effective polynomial-time heuristics that, for many instances, can find the exact MWT. Linear programs (LPs) for MWT are well-...

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ ...

Helly's theorem says that, if every $d+1$ elements of a given finite set of convex objects in $\mathbb{R}^d$ have a common point, there is a point common to all of the objects in the set. In discrete Helly theorems the common point should belong to an a ...

We give the first algorithmic study of a class of "covering tour" problems related to the geometric traveling salesman problem: Find a polygonal tour for a cutter so that it sweeps out a specified region ("pocket") in order to minimize a cost that ...

Two decades ago, Megiddo and Dyer showed that linear programming (LP) in two and three dimensions (and subsequently any constant number of dimensions) can be solved in linear time. In this paper, we consider the LP problem with at most k violations, ...

We consider parallel, identical machine scheduling problems, where the jobs are subject to precedence constraints and release dates, and where the processing times of jobs are governed by independent probability distributions. Our objective is to ...

We present improved combinatorial approximation algorithms for the uncapacitated facility location problem. Two central ideas in most of our results are cost scaling and greedy improvement. We present a simple greedy local search algorithm which ...

We investigate the worst-case behavior of the simplex algorithm on linear programs with three variables, that is, on 3-dimensional simple polytopes. Among the pivot rules that we consider, the "random edge" rule yields the best asymptotic behavior as ...

In the 0-extension problem, we are given a weighted graph with some nodes marked as terminals and a semimetric on the set of terminals. Our goal is to assign the rest of the nodes to terminals so as to minimize the sum, over all edges, of the product of ...

We study combinatorial optimization problems in which a set of distributed agents must achieve a global objective using only local information. Papadimitriou and Yannakakis [Proceedings of the 25th ACM Symposium on Theory of Computing, 1993, pp. 121--...

Local search algorithms for combinatorial optimization problems are generally of pseudopolynomial running time, and polynomial-time algorithms are not often known for finding locally optimal solutions for NP-hard optimization problems. We introduce the ...

We introduce a natural variant of the (metric uncapacitated) k-median problem that we call the online median problem. Whereas the k-median problem involves optimizing the simultaneous placement of k facilities, the online median problem imposes the ...

We present the first constant-factor approximation algorithm for a fundamental problem: the store-and-forward packet routing problem on arbitrary networks. Furthermore, the queue sizes required at the edges are bounded by an absolute constant. Thus, ...

We describe a deterministic parallel algorithm for linear programming in fixed dimension d that takes poly(log log n) time in the common concurrent read concurrent write (CRCW) PRAM model and does optimal O(n) work. In the exclusive read exclusive write ...

We present a linear programming-based method for finding "gadgets," i.e., combinatorial structures reducing constraints of one optimization problem to constraints of another. A key step in this method is a simple observation which limits the search ...