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Backtracking is a basic strategy to solve constraint satisfaction problems (CSPs). A satisfiable CSP instance is backtrack-free if a solution can be found without encountering any dead-end during a backtracking search, implying that the instance is easy to solve. We prove an exact phase transition of backtrack-free search in some random CSPs, namely in Model RB and in Model RD. This is the first time an exact phase transition of backtrack-free search can be identified on some random CSPs. Our technical results also have interesting implications on the power of greedy algorithms, on the width of random hypergraphs and on the exact satisfiability threshold of random CSPs.
We study the problem of finding large cuts in $d$-regular triangle-free graphs. In prior work, Shearer (1992) gives a randomised algorithm that finds a cut of expected size $(1/2 + 0.177/sqrt{d})m$, where $m$ is the number of edges. We give a simpler
Given a clique-width $k$-expression of a graph $G$, we provide $2^{O(k)}cdot n$ time algorithms for connectivity constraints on locally checkable properties such as Node-Weighted Steiner Tree, Connected Dominating Set, or Connected Vertex Cover. We a
We consider a multi-agent model for fair division of mixed manna (i.e. items for which agents can have positive, zero or negative utilities), in which agents have additive utilities for bundles of items. For this model, we give several general imposs
MAXCUT defines a classical NP-hard problem for graph partitioning and it serves as a typical case of the symmetric non-monotone Unconstrained Submodular Maximization (USM) problem. Applications of MAXCUT are abundant in machine learning, computer vis
For a graph $G=(V,E)$, $kin mathbb{N}$, and a complex number $w$ the partition function of the univariate Potts model is defined as [ {bf Z}(G;k,w):=sum_{phi:Vto [k]}prod_{substack{uvin E phi(u)=phi(v)}}w, ] where $[k]:={1,ldots,k}$. In this paper w