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We present an improved "cooling schedule" for simulated annealing algorithms for combinatorial counting problems. Under our new schedule the rate of cooling accelerates as the temperature decreases. Thus, fewer intermediate temperatures are needed as the simulated annealing algorithm moves from the high temperature (easy region) to the low temperature… (More)

- Marcus Schaefer, Eric Sedgwick, Daniel Stefankovic
- STOC
- 2002

A <i>string graph</i> is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in <b>NP</b>. The recognition problem was not known to be decidable until very recently, when two independent… (More)

- Qi Ge, Daniel Stefankovic
- FSTTCS
- 2010

We introduce a new graph polynomial that encodes interesting properties of graphs, for example, the number of matchings, the number of perfect matchings, and, for bipartite graphs, the number of independent sets (#BIS). We analyse the complexity of exact evaluation of the polynomial at rational points and show a dichotomy result: for most points exact… (More)

- Michael J. Pelsmajer, Marcus Schaefer, Daniel Stefankovic
- J. Comb. Theory, Ser. B
- 2007

An edge in a drawing of a graph is called even if it intersects every other edge of the graph an even number of times. Pach and Tóth proved that a graph can always be redrawn such that its even edges are not involved in any intersections. We give a new, and significantly simpler, proof of a slightly stronger statement. We show two applications of this… (More)

- Michael J. Pelsmajer, Marcus Schaefer, Daniel Stefankovic
- Algorithmica
- 2009

We show that computing the crossing number and the odd crossing number of a graph with a given rotation system is NP-complete. As a consequence we can show that many of the well-known crossing number notions are NP-complete even if restricted to cubic graphs (with or without rotation system). In particular, we can show that Tutte’s independent odd crossing… (More)

- Marcus Schaefer, Daniel Stefankovic
- J. Comput. Syst. Sci.
- 2001

We show that string graphs can be recognized in nondeterministic exponential time by giving an exponential upper bound on the number of intersections for a drawing realizing the string graph in the plane. This upper bound confirms a conjecture by Kratochv\'{\i}l and Matou\v{s}ek~\cite{KM91} and settles the long-standing open problem of the decidability of… (More)

- László Babai, Amir Shpilka, Daniel Stefankovic
- IEEE Transactions on Information Theory
- 2003

Cyclic linear codes of block length n over a finite field F/sub q/ are linear subspaces of F/sub q//sup n/ that are invariant under a cyclic shift of their coordinates. A family of codes is good if all the codes in the family have constant rate and constant normalized distance (distance divided by block length). It is a long-standing open problem whether… (More)

- Marcus Schaefer, Daniel Stefankovic
- Theory of Computing Systems
- 2015

We introduce the complexity class ∃ ℝ $\exists \mathbb {R}$ based on the existential theory of the reals. We show that the definition of ∃ ℝ $\exists \mathbb {R}$ is robust in the sense that even the fragment of the theory expressing solvability of systems of strict polynomial inequalities leads to the same complexity class. Several natural and well-known… (More)

- Andreas Galanis, Qi Ge, Daniel Stefankovic, Eric Vigoda, Linji Yang
- Random Struct. Algorithms
- 2011

We study the computational complexity of approximately counting the number of independent sets of a graph with maximum degree Δ. More generally, for an input graph G = (V,E) and an activity λ > 0, we are interested in the quantity ZG(λ) defined as the sum over independent sets I weighted as w(I) = λ|I|. In statistical physics, ZG(λ) is the partition… (More)

- Andreas Galanis, Daniel Stefankovic, Eric Vigoda
- Combinatorics, Probability & Computing
- 2016

Recent inapproximability results of Sly (2010), together with an approximation algorithm presented by Weitz (2006) establish a beautiful picture for the computational complexity of approximating the partition function of the hard-core model. Let λc(T∆) denote the critical activity for the hard-model on the infinite ∆-regular tree. Weitz presented an FPTAS… (More)