Max-Cut in planar graphs is NL-hard; 4. $\\\oplus $ Directed-spanning-trees in planar graphs is $\\\oplus $L-complete. For (1) we analyze the space complexity of the well known Baker's algorithm [1] using a recent result of Elberfeld, Jakoby, and Tantau [13] that gives a Log...
In particular, each iteration of the proposed algorithm requires to solve the hidden convex problems. The computational complexity is linear with the number of iterations and polynomial with the sizes of the STTW and the STRF. Finally, the gain and the computation ...
This means that after sufficient time, subject to the complexity of the problem, the solutions are good enough for use, which may not be strictly optimal though. This is a great boon as the exact methods would not even have managed to return a single solution. The sampling-based motion ...
The cooperation of the three branches makes more simple and clear statements on basic problems in cognition science and obtains more simple and fast algorithms; the N-harp problems mentioned above can be resolved by at most O(m2n) complexity, where m, n are numbers of objects and factors ...
In one-hot encoding, although the implementation is easy and straightforward, space complexity is very high for large vocabulary size. In our example, we have a limited number of dimensions in vector space. However, in a vocabulary with a size of 10 million words, the representations of words...
even the state-of-the-art algorithms developed for the NISQ era often suffer from high space complexity requirements for particular problem classes. In this paper, we show that it is possible to greatly reduce the number of qubits needed for the Travelling Salesman Problem (TSP), a paradigmatic...
We can express the algorithm we want to apply as a node represents a winning state if there is a way to transform it into a sequence of n distinct elements. or more formally: Equivalently in swift:let isWon = adjacency.contains { [node, n] adjacency in Set(sequence(first: node) { ...
performance properties are investigated by numerical experiments of increasing complexity. Our numerical experiments confirm that GMRES iterations that are preconditioned by the proposed GMG method converge at a desired rate that is (nearly) independent of the mesh sizes in space and time; cf. also [...
We observe that in Lemma 2.1 the nτ-factor in the time complexity is due to matching X in the sampled suffix tree STi by passing the string τ times, each time with a different choice of j∈[1,τ], j≠i. Each such pass costs us O(nlognτ) time. The idea is to reduce th...
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