Data structures and network algorithms
Data structures and network algorithms
Graph minors. V. Excluding a planar graph
Journal of Combinatorial Theory Series B
Linear time algorithms for NP-hard problems restricted to partial k-trees
Discrete Applied Mathematics
Finding approximate separators and computing tree width quickly
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Quickly excluding a planar graph
Journal of Combinatorial Theory Series B
Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Approximations for the disjoint paths problem in high-diameter planar networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Handbook of combinatorics (vol. 1)
Decision algorithms for unsplittable flow and the half-disjoint paths problem
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Highly connected sets and the excluded grid theorem
Journal of Combinatorial Theory Series B
Improved Approximation Algorithms for Unsplittable Flow Problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Graph minors. XVI. excluding a non-planar graph
Journal of Combinatorial Theory Series B
Edge-Disjoint Paths in Planar Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
The equivalence of theorem proving and the interconnection problem
ACM SIGDA Newsletter
Algorithmic Graph Minor Theory: Decomposition, Approximation, and Coloring
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Edge-disjoint paths in Planar graphs with constant congestion
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Packing Non-Zero A-Paths In Group-Labelled Graphs
Combinatorica
Non-zero disjoint cycles in highly connected group labelled graphs
Journal of Combinatorial Theory Series B
A nearly linear time algorithm for the half integral disjoint paths packing
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Some remarks on the odd hadwiger’s conjecture
Combinatorica
On the odd-minor variant of Hadwiger's conjecture
Journal of Combinatorial Theory Series B
Note: Note on coloring graphs without odd-Kk-minors
Journal of Combinatorial Theory Series B
Combinatorica
An improved algorithm for finding cycles through elements
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Finding odd cycle transversals
Operations Research Letters
Proceedings of the forty-second ACM symposium on Theory of computing
Subexponential algorithms for partial cover problems
Information Processing Letters
Parameterized tractability of multiway cut with parity constraints
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.01 |
We consider the following problem, which is called the half integral parity disjoint paths packing problem. Input: A graph G, k pair of vertices (s1, t1), (s2, t2), ...,(sk, tk) in G (which are sometimes called terminals), and a parity li for each i with 1 ≤ i ≤ k, where li = 0 or 1. Output: Paths P1, ..., Pk in G such that Pi joins si and ti for i = 1, 2, ..., k and parity of length of the path Pi is li, i.e, if li = 0, then length of Pi is even, and if li = 1, then length of Pi is odd for i = 1, 2, ..., k. In addition, each vertex is on at most two of these paths. We present an O(mα(m, n) log n) algorithm for fixed k, where n, m are the number of vertices and the number of edges, respectively, and the function α(m, n) is the inverse of the Ackermann function (see by Tarjan [43]). This is the first polynomial time algorithm for this problem, and generalizes polynomial time algorithms by Kleinberg [23] and Kawarabayashi and Reed [20], respectively, for the half integral disjoint paths packing problem, i.e., without the parity requirement. As with the Robertson-Seymour algorithm to solve the k disjoint paths problem, in each iteration, we would like to either use a huge clique minor as a "crossbar", or exploit the structure of graphs in which we cannot find such a minor. Here, however, we must maintain the parity of the paths and can only use an "odd clique minor". We must also describe the structure of those graphs in which we cannot find such a minor and discuss how to exploit it. We also have algorithms running in O(m(1 + ε)) time for any ε 0 for this problem, if k is up to o(log log log n) for general graphs, up to o(log log n) for planar graphs, and up to o(log log n/g) for graphs on the surface, where g is Euler genus. Furthermore, if k is fixed, then we have linear time algorithms for the planar case and for the bounded genus case.