This paper concerns the folded concave penalized sparse linear regression (FCPSLR), a class of popular sparse recovery methods. Although FCPSLR yields desirable recovery performance when solved globally, computing a global solution is NP-complete. Despite some existing statistical performance analyses on local minimizers or on specific FCPSLR-based learning algorithms, it still remains open que...

Given a combinatorial decomposition for a counting problem, we resort to the simplescheme of approximating large numbers by floating-point representations in order to obtainefficient Fully Polynomial Time Approximation Schemes (FPTASes) for it. The numberof bits employed for the exponent and the mantissa will depend on the error parameter0 < ε ≤ 1 and on the characteristics ...

We study the fundamental problem of computing an arbitrary Nash equilibrium in bimatrix games. We start by proposing a novel characterization of the set of Nash equilibria, via a bijective map to the solution set of a (parameterized) quadratic program, whose feasible space is the (highly structured) set of correlated equilibria. We then proceed by proposing new subclasses of bimatrix games for ...

We propose a notion of contraction function for a family of graphs and establish its connection to the strong spatial mixing for spin systems. More specifically, we show that for anti-ferromagnetic Potts model on families of graphs characterized by a specific contraction function, the model exhibits strong spatial mixing, and if further the graphs exhibit certain local sparsity which are very n...

Assortment optimization refers to the problem of designing a slate products offer potential customers, such as stocking shelves in convenience store. The price each product is fixed advance, and probabilistic choice function describes which customer will choose from any given subset. We introduce combinatorial assortment problem, where may select bundle products. consider model consumer selects...

The pagination problem is described as follows. We have a set of symbols, collection subsets over these symbols (we call the tiles) and an integer capacity C . objective to find minimal number pages (a type container) on which we can schedule all tiles while following two fundamental rules. cannot assign more than each page tile be broken into several pieces, its must assigned at least one page...

We introduce the Destructive Object Handling (DOH) problem, which models aspects of many real-world allocation problems, such as shipping explosive munitions, scheduling processes in a cluster with fragile nodes, re-using passwords across multiple websites, and quarantining patients during a disease outbreak. In these problems, objects must be assigned to handlers, but each object has a probabi...

We study the interval knapsack problem (I-KP), and the interval multiple-choice knapsack problem (I-MCKP), as generalizations of the classic 0/1 knapsack problem (KP) and the multiple-choice knapsack problem (MCKP), respectively. Compared to singleton items in KP and MCKP, each item i in I-KP and I-MCKP is represented by a ([ai, bi], pi) pair, where integer interval [ai, bi] specifies the possi...