Related papers: FPTAS for Weighted Fibonacci Gates and Its Applica…
We show for a broad class of counting problems, correlation decay (strong spatial mixing) implies FPTAS on planar graphs. The framework for the counting problems considered by us is the Holant problems with arbitrary constant-size domain…
We give the first deterministic fully polynomial-time approximation scheme (FPTAS) for computing the partition function of a two-state spin system on an arbitrary graph, when the parameters of the system satisfy the uniqueness condition on…
Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin…
A monotone CNF formula is a Boolean formula in conjunctive normal form where each variable appears positively. We design a deterministic fully polynomial-time approximation scheme (FPTAS) for counting the number of satisfying assignments…
Given a combinatorial decomposition for a counting problem, we resort to the simple scheme of approximating large numbers by floating-point representations in order to obtain efficient Fully Polynomial Time Approximation Schemes (FPTASes)…
In this paper, we investigate the parametric weight knapsack problem, in which the item weights are affine functions of the form $w_i(\lambda) = a_i + \lambda \cdot b_i$ for $i \in \{1,\ldots,n\}$ depending on a real-valued parameter…
In this thesis we develop FPTASs for the counting problems of m-tuples, contingency tables with two rows, and 0/1 knapsack. For the problem of counting m-tuples, we design two algorithms, one is strongly polynomial. As far as we know, these…
Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among…
We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…
Valiant introduced matchgate computation and holographic algorithms. A number of seemingly exponential time problems can be solved by this novel algorithmic paradigm in polynomial time. We show that, in a very strong sense, matchgate…
We address the classical knapsack problem and a variant in which an upper bound is imposed on the number of items that can be selected. We show that appropriate combinations of rounding techniques yield novel and powerful ways of rounding.…
We give fully polynomial-time approximation schemes (FPTAS) for the partition function of ferromagnetic 2-spin systems in certain parameter regimes. The threshold we obtain is almost tight up to an integrality gap. Our technique is based on…
In this paper, we investigate the parametric knapsack problem, in which the item profits are affine functions depending on a real-valued parameter. The aim is to provide a solution for all values of the parameter. It is well-known that any…
Holant problems are a general framework to study the algorithmic complexity of counting problems. Both counting constraint satisfaction problems and graph homomorphisms are special cases. All previous results of Holant problems are over the…
It is known that there is no EPTAS for the $m$-dimensional knapsack problem unless $W[1] = FPT$. It is true already for the case, when $m = 2$. But, an FPTAS still can exist for some other particular cases of the problem. In this note, we…
We prove a complexity dichotomy for complex-weighted Holant problems with an arbitrary set of symmetric constraint functions on Boolean variables. This dichotomy is specifically to answer the question: Is the FKT algorithm under a…
The subject of this paper is the time complexity of approximating Knapsack, Subset Sum, Partition, and some other related problems. The main result is an $\widetilde{O}(n+1/\varepsilon^{5/3})$ time randomized FPTAS for Partition, which is…
Generalized counting constraint satisfaction problems include Holant problems with planarity restrictions; polynomial-time algorithms for such problems include matchgates and matchcircuits, which are based on Pfaffians. In particular, they…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
In a widely-studied class of multi-parametric optimization problems, the objective value of each solution is an affine function of real-valued parameters. Then, the goal is to provide an optimal solution set, i.e., a set containing an…