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- 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)

- 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)

- Parikshit Gopalan, Adam R. Klivans, Raghu Meka, Daniel Stefankovic, Santosh Vempala, Eric Vigoda
- 2011 IEEE 52nd Annual Symposium on Foundations of…
- 2011

Given $n$ elements with non-negative integer weights $w_1,..., w_n$ and an integer capacity $C$, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most $C$. We give the first deterministic, fully polynomial-time approximation scheme (FPTAS) for estimating the number of solutions… (More)

- Daniel Stefankovic, Santosh Vempala, Eric Vigoda
- SIAM J. Comput.
- 2012

Given n elements with nonnegative integer weights w 1 ,. .. , wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given capacity. We give a deterministic algorithm that estimates the number of solutions to within relative error 1 ± ε in time… (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)

- 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)

- 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)

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)

- Daniel Stefankovic, Santosh Vempala, Eric Vigoda
- 48th Annual IEEE Symposium on Foundations of…
- 2007

We present a near-optimal reduction from approximately counting the cardinality of a discrete set to approximately sampling elements of the set. An important application of our work is to approximating the partition function <i>Z</i> of a discrete system, such as the Ising model, matchings or colorings of a graph. The typical approach to estimating the… (More)

- Michael J. Pelsmajer, Marcus Schaefer, Daniel Stefankovic
- Discrete & Computational Geometry
- 2008

The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the odd crossing number. We show that there is a graph for which these two concepts differ, answering a… (More)