Scheduling partially ordered jobs faster than 2n
ESA'11 Proceedings of the 19th European conference on Algorithms
Shortest cycle through specified elements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Improved simulation of nondeterministic Turing machines
Theoretical Computer Science
On cutwidth parameterized by vertex cover
IPEC'11 Proceedings of the 6th international conference on Parameterized and Exact Computation
Solving the 2-disjoint connected subgraphs problem faster than 2n
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Approximating MAX SAT by moderately exponential and parameterized algorithms
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Parameterized complexity and subexponential-time computability
The Multivariate Algorithmic Revolution and Beyond
What's next? future directions in parameterized complexity
The Multivariate Algorithmic Revolution and Beyond
Reducing a target interval to a few exact queries
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
On exact algorithms for treewidth
ACM Transactions on Algorithms (TALG)
A fast parallel algorithm for minimum-cost small integral flows
Euro-Par'12 Proceedings of the 18th international conference on Parallel Processing
Finding a maximum induced degenerate subgraph faster than 2n
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Homomorphic hashing for sparse coefficient extraction
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Fast monotone summation over disjoint sets
IPEC'12 Proceedings of the 7th international conference on Parameterized and Exact Computation
Communications of the ACM
Fast hamiltonicity checking via bases of perfect matchings
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On testing monomials in multivariate polynomials
Theoretical Computer Science
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Faster exponential-time algorithms in graphs of bounded average degree
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Exponential approximation schemata for some network design problems
Journal of Discrete Algorithms
Finding the minimum-weight k-path
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
On exact algorithms for the permutation CSP
Theoretical Computer Science
Kernel bounds for path and cycle problems
Theoretical Computer Science
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We present a Monte Carlo algorithm for Hamilton city detection in an $n$-vertex undirected graph running in $O^*(1.657^{n})$ time. To the best of our knowledge, this is the first super polynomial improvement on the worst case runtime for the problem since the $O^*(2^n)$ bound established for TSP almost fifty years ago (Bellman 1962, Held and Karp 1962). It answers in part the first open problem in Woe ginger's 2003 survey on exact algorithms for NP-hard problems. For bipartite graphs, we improve the bound to $O^*(1.414^{n})$ time. Both the bipartite and the general algorithm can be implemented to use space polynomial in $n$. We combine several recently resurrected ideas to get the results. Our main technical contribution is a new reduction inspired by the algebraic sieving method for $k$-Path (Koutis ICALP 2008, Williams IPL 2009). We introduce the Labeled Cycle Cover Sum in which we are set to count weighted arc labeled cycle covers over a finite field of characteristic two. We reduce Hamiltonicity to Labeled Cycle Cover Sum and apply the determinant summation technique for Exact Set Covers (Bj\"orklund STACS 2010) to evaluate it.