Edge cover games are cooperative cost games arising from edge cover problems, where each player controls a vertex and the cost of a coalition is the minimum weight of edge covers in the subgraph induced by the coalition. In this paper, we study ...$\frac{\mathrm{}}{\mathrm{}}$$\frac{\mathrm{}}{\mathrm{}}$

In this paper, we bound the integrality gap and the approximation ratio for maximum plane multiflow problems and deduce bounds on the flow-multicut-gap. We consider instances where the union of the supply and demand graphs is planar and prove that ...

We relate discrepancy theory with the classic scheduling problems of minimizing max flow time and total flow time on unrelated machines. Specifically, we give a general reduction that allows us to transfer discrepancy bounds in the prefix Beck-Fiala (...

The traveling salesman problem (TSP) is a fundamental problem in combinatorial optimization. Several semidefinite programming relaxations have been proposed recently that exploit a variety of mathematical structures including, for example, algebraic ...

We consider the 0-Extension problem, where we are given an undirected graph G=(V,E) equipped with non-negative edge weights w:E→ ℝ⁺, a collection T={ t₁,…,t_k}⊆ V of k special vertices called terminals, and a semi-metric D over T. The goal is to assign ...

The Restricted Assignment problem is a prominent special case of Scheduling on Unrelated Parallel Machines. For the strongest known linear programming relaxation, the configuration LP, we improve the nonconstructive bound on its integrality gap from 1.9412 to ...

We give a new, strongly polynomial-time algorithm and improved analysis for the metric s-t path Traveling Salesman Problem (TSP). It finds a tour of cost less than 1.53 times the optimum of the subtour elimination linear program (LP), while known ...

We consider the integrality gap of the subtour linear program (LP) relaxation of the traveling salesman problem (TSP) restricted to circulant instances. De Klerk and Dobre [Discrete Appl. Math., 159 (2011), pp. 1815--1826] conjectured that the value of ...

We study the approximability of constraint satisfaction problems (CSPs) by linear programming (LP) relaxations. We show that for every CSP, the approximation obtained by a basic LP relaxation, is no weaker than the approximation obtained using ...

We consider the maximum flow network interdiction problem in its cardinality case. There is an integer programming model for this problem by Wood Math Comput Model 17 1993, 1-18. Two types of valid inequalities have also been proposed Altner et al., ...

We consider the classical problem of Scheduling on Unrelated Machines. In this problem a set of jobs is to be distributed among a set of machines and the maximum load (makespan) is to be minimized. The processing time p_ij of a job j depends on the ...

Given a complete graph $K_{n}=(V, E)$ with nonnegative edge costs $c\in {\mathbb R}^{E}$, the problem 2EC is that of finding a 2-edge connected spanning multisubgraph of $K_{n}$ of minimum cost. The integrality gap $\alpha\text{2{\it EC}}$ of the linear ...

We propose a candidate reduction for ruling out polynomial-time algorithms for unique games, either under plausible complexity assumptions, or unconditionally for Lasserre semi-definite programs with a constant number of rounds. We analyze the ...

We examine cooperative games where the viability of a coalition is determined by whether or not its members have the ability to communicate amongst themselves independently of non-members. This necessary condition for viability was proposed by Myerson [...

In this article, we disprove a conjecture of Goemans and Linial; namely, that every negative type metric embeds into ℓ₁ with constant distortion. We show that for an arbitrarily small constant δ > 0, for all large enough n, there is an n-point negative ...

We show (under standard assumptions) that there are \textsf{NP} optimization problems for which estimation is easier than approximation. Namely, one can estimate the value of the optimal solution within a ratio of $\rho$, but it is difficult to find a ...

After a sequence of improvements Boyd et al. [TSP on cubic and subcubic graphs, Integer Programming and Combinatorial Optimization, Lecture Notes in Comput. Sci. 6655, Springer, Heidelberg, 2011, pp. 65--77] proved that any 2-connected graph whose $n$ ...

Determining the precise integrality gap for the subtour linear programming (LP) relaxation of the traveling salesman problem is a significant open question, with little progress made in thirty years in the general case of symmetric costs that obey ...

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-...

<P>We consider cooperative traveling salesman games with nonnegative asymmetric costs satisfying the triangle inequality. We construct a stable cost allocation with budget balance guarantee equal to the Held-Karp integrality gap for the asymmetric ...