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- Marek Cygan, Jakub W. Pachocki, Arkadiusz Socala
- ArXiv
- 2015

Subgraph Isomorphism is a very basic graph problem, where given two graphs G and H one is to check whether G is a subgraph of H . Despite its simple definition, the Subgraph Isomorphism problem turns out to be very broad, as it generalizes problems such as Clique, r-Coloring, Hamiltonicity, Set Packing and Bandwidth. However, for all of the mentioned… (More)

- Marthe Bonamy, Lukasz Kowalik, Michal Pilipczuk, Arkadiusz Socala
- Algorithmica
- 2015

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)

- Marek Cygan, Fedor V. Fomin, +4 authors Arkadiusz Socala
- SODA
- 2016

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)

- Arkadiusz Socala
- SODA
- 2015

We study the complexity of the C<scp>hannel</scp> A<scp>ssignment</scp> problem. An open problem asks whether C<scp>hannel</scp> A<scp>ssignment</scp> admits an <i>O</i>(<i>c<sup>n</sup></i>) (times a polynomial in the bit size) time algorithm, where <i>n</i> is a number of the vertices, for a constant <i>c</i> independent of the weights on the edges. We… (More)

- Lukasz Kowalik, Arkadiusz Socala
- Algorithmica
- 2014

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)

- Marek Cygan, Fedor V. Fomin, +4 authors Arkadiusz Socala
- J. ACM
- 2017

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 |<i>V</i>(<i>H</i>)|<sup><i>o</i>(|<i>V</i>(<i>G</i>)|)</sup>. We also show an exponential-time reduction from Graph Homomorphism to Subgraph Isomorphism. This rules… (More)

- Lukasz Kowalik, Juho Lauri, Arkadiusz Socala
- ESA
- 2016

The Rainbow k-Coloring problem asks whether the edges of a given graph can be colored in k colors so that every pair of vertices is connected by a rainbow path, i.e., a path with all edges of different colors. Our main result states that for any k ≥ 2, there is no algorithm for Rainbow k-Coloring running in time 2 3/2), unless ETH fails. Motivated by this… (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)

- Marek Cygan, Lukasz Kowalik, Arkadiusz Socala
- ESA
- 2017

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)