Bin packing asks whether a collection of items can be packed into at most a given number of bins of a given capacity. We consider the high-multiplicity setting with $d$ distinct item sizes, in which both the item sizes and the number of items of each size are encoded in binary. Goemans and Rothvos (JACM 2020) gave an X...
We give a randomized algorithm for Directed Hamiltonian Cycle on $n$-vertex directed graphs that runs in time $O^*((375/196)^n)=O^*(1.9133^n)$. For general directed graphs, this is the first improvement in the exponential base over the classical $O^*(2^n)$-time algorithms of Bellman and Held--Karp (1962). To obtain thi...
The SCA problem can be solved in time and admits a polynomial kernel with vertices and bits and the algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.
This analysis builds on the biased-metric viewpoint behind the recent improvement over the $3$ barrier and proves a stability property for the biased-metric ratio.
Shinsaku Sakaue, K. Fujii, Soh Kumabe et al.· arXiv.org· 0 citations
The problem is reduced to a boundary-pair variant of $2-vertex-connected spanning subgraph, where each vertex is assigned a pair of incident edges with an associated pair cost, and a deterministic algorithm is given with running time $O^*(36^kW)$.
The results reveal that, in this setting, MCIS is strictly harder than ISI, and it is shown that it becomes NP-hard already when each input graph has cluster vertex deletion number 2.
Tomohiro Koana, Soh Kumabe, Y. Otachi· 0 citations
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