We define a matrix concept we call factor width. This gives a hierarchy of matrix classes for symmetric positive semidefinite matrices, or a set of nested cones. We prove that the set of symmetric… Expand

A tree (tour) cover of an edge-weighted graph is a set of edges which forms a tree and covers every other edge in the graph and an approximation algorithm with ratios 3.55 and 5.5 is presented.Expand

A unified framework for approximating problems that can be formulated or interpreted as special cases of generalized partial cover is presented, and the applicability of the method is demonstrated on a diverse collection of covering problems, for some of which the first non-trivial approximability results are obtained.Expand

A simple 2 1/10 -approximation algorithm for the weighted edge-dominating set problem, improving the existing ratio, due to a simple reduction to weighted vertex cover, of 2rWVC, where rWVC is the approximation guarantee of any polynomial-time weighted vertices cover algorithm.Expand

The bipartite algorithmic integrality gap upper bound is used, showing that for the family of combinatorial auctions in which anyone can win at most $t$ items, there is a truthful-in-expectation polynomial-time auction that $t-approximately maximizes social welfare.Expand

A unified framework for approximating problems that can be formulated or interpreted as special cases of generalized partial cover is presented, and the applicability of the method on a diverse collection of covering problems is demonstrated, for some of which the first non-trivial approximability results are obtained.Expand

The results show that improving the approximation factor beyond 8/3 using the approach of adding valid inequalities to a natural linear programming relaxation is as hard as improving the approximate factor for vertex cover beyond 2.Expand

A simple approximability algorithm for the weighted edge-dominating set problem, improving the existing ratio, due to a simple reduction to weighted vertex cover, of 2rWVC, where rWVC is the approximation guarantee of any polynomial-time weighted vertices cover algorithm.Expand

A simple iterative packing technique that retains features of Jain's seminal approach, including the property that the magnitude of the fractional value of the element rounded during each iteration has a direct impact on the approximation guarantee.Expand

We lay the foundation for a benchmarking methodology for assessing current and future quantum computers. We pose and begin addressing fundamental questions about how to fairly compare computational… Expand