Holographic algorithms with matchgates are a novel approach to design polynomial time computation. It uses Kasteleyn's algorithm for perfect matchings, and more importantly a holographic reduction. The two fundamental parameters of a holographic reduction are the domain size k of the underlying problem, and the basis size ℓ. A holographic reduction… (More)
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 holographic transformation  a universal strategy to obtain polynomial-time algorithms for problems over planar graphs that… (More)
BACKGROUND This study aimed to compare the surgical outcomes between open pedicle screw fixation (OPSF) and percutaneous pedicle screw fixation (PPSF) for the treatment of thoracolumbar fractures, which has received scant research attention to date. MATERIAL AND METHODS Eight-four patients with acute and subacute thoracolumbar fractures who were treated… (More)
We prove a complexity classification theorem that classifies all counting constraint satisfaction problems (#CSP) over Boolean variables into exactly three categories: (1) Polynomial-time tractable; (2) #P-hard for general instances, but solvable in polynomial-time over planar graphs; and (3) #P-hard over planar graphs. The classification applies to all… (More)
Research Interests • Computational complexity. Exact and approximate counting algorithms and hardness.
An essential problem in the design of holographic algorithms is to decide whether the required signatures can be realized by matchgates under a suitable basis transformation (SRP). For holographic algorithms on domain size 2, [1, 2, 4, 5] have built a systematical theory. In this paper, we reduce SRP on domain size k ≥ 3 to SRP on domain size 2 for… (More)