Arkadiusz Socala

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In the $$k$$ k -Leaf Out-Branching and $$k$$ k -Internal Out-Branching problems we are given a directed graph D with a designated root r and a nonnegative integer k. The question is whether there exists an outbranching rooted at r that has at least k leaves, or at least k internal vertices, respectively. Both these problems have been studied from the points(More)
We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time |V (H)|o(|V (G)|). We also show an exponential-time reduction from Graph Homomorphism to Subgraph Isomorphism. This rules out (subject to ETH) a possibility of |V (H)|o(|V (H)|)-time algorithm deciding if graph G(More)
We study the complexity of the Channel Assignment problem. By applying the meet-in-the-middle approach we get an algorithm for the $$\ell $$ ℓ -bounded Channel Assignment (when the edge weights are bounded by $$\ell $$ ℓ ) running in time $$O^*((2\sqrt{\ell +1})^n)$$ O ∗ ( ( 2 ℓ + 1 ) n ) . This is the first algorithm which breaks the $$(O(\ell ))^n$$ ( O ((More)
We present three results on the complexity of Minimax Approval Voting. First, we study Minimax Approval Voting parameterized by the Hamming distance d from the solution to the votes. We show Minimax Approval Voting admits no algorithm running in time O(2 log ), unless the Exponential Time Hypothesis (ETH) fails. This means that the O(d) algorithm of Misra(More)
We prove that unless the Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph <i>G</i> to graph <i>H</i> cannot be done in time &verbar;<i>V</i>(<i>H</i>)&verbar;<sup><i>o</i>(&verbar;<i>V</i>(<i>G</i>)&verbar;)</sup>. We also show an exponential-time reduction from Graph Homomorphism to Subgraph Isomorphism. This rules(More)
In the multicoloring problem, also known as (a:b)-coloring or b-fold coloring, we are given a graph G and a set of a colors, and the task is to assign a subset of b colors to each vertex of G so that adjacent vertices receive disjoint color subsets. This natural generalization of the classic coloring problem (the b = 1 case) is equivalent to finding a(More)
Given a traveling salesman problem (TSP) tour H in graph G a k-move is an operation which removes k edges from H , and adds k edges of G so that a new tour H ′ is formed. The popular k-OPT heuristic for TSP finds a local optimum by starting from an arbitrary tour H and then improving it by a sequence of k-moves. Until 2016, the only known algorithm to find(More)