Light Spanner and Monotone Tree

  title={Light Spanner and Monotone Tree},
  author={Hao-Hsiang Hung},
In approximation algorithm design, light spanners has applications in graph-metric problems such as metric TSP (the traveling salesman problem) [8] and others [3]. We have developed an efficient algorithm in [9] for light spanners in bounded pathwidth graphs, based on an intermediate data structure called monotone tree. In this paper, we extended the results to include bounded catwidth graphs. 

A Light Metric Spanner

  • Lee-Ad Gottlieb
  • Mathematics
    2015 IEEE 56th Annual Symposium on Foundations of Computer Science
  • 2015
This paper shows that doubling spaces admit (1 + ε)-stretch spanners with lightness WD = (ddim /ε)<sup>O(ddim)</sup>.

Minor-Free Graphs Have Light Spanners

We show that every H-minor-free graph has a light (1+&#x2265;ilon)-spanner, resolving an open problem of Grigni and Sissokho and proving a conjecture of Grigni and Hung \cite{GH12}. Our lightness

The Greedy Spanner is Existentially Optimal

It is concluded that the greedy spanner achieves near-optimal weight guarantees for both general graphs and doubling metrics, thus resolving two longstanding conjectures in the area.

The Greedy Spanner is Existentially Optimal [ Extended

It is concluded that the greedy spanner achieves near-optimal weight guarantees for both general graphs and doubling metrics, thus resolving two longstanding conjectures in the area.



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A linear time algorithm exactly solving the 2-edge connected spanning subgraph (2-ECSS) problem in a graph of bounded treewidth is presented, and the first PTAS for the problem in weighted planar graphs is found.

On sparse spanners of weighted graphs

This paper gives a simple algorithm for constructing sparse spanners for arbitrary weighted graphs and applies this algorithm to obtain specific results for planar graphs and Euclidean graphs.

A polynomial-time approximation scheme for weighted planar graph TSP

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Approximate TSP in Graphs with Forbidden Minors

A QPTAS (quasi-polynomial time approximation scheme) for the TSP (traveling salesperson problem) in unweighted graphs with an excluded minor in weighted graphs with bounded genus is implied.

A linear-time approximation scheme for planar weighted TSP

  • P. Klein
  • Computer Science
    46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)
  • 2005
An algorithm requiring O(c/sup 1/c2/ n) time to find an /spl epsi/-optimal traveling salesman tour in the metric defined by a planar graph with nonnegative edge-lengths is given.

The Traveling Salesman Problem with Distances One and Two

We present a polynomial-time approximation algorithm with worst-case ratio 7/6 for the special case of the traveling salesman problem in which all distances are either one or two. We also show that

Solving Connectivity Problems Parameterized by Treewidth in Single Exponential Time

It is shown that the aforementioned gap cannot be breached for some problems that aim to maximize the number of connected components like Cycle Packing, and in several cases it is able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail.

Finding Light Spanners in Bounded Pathwidth Graphs

This paper shows that light spanners exist for graphs with bounded pathwidth, via the construction of light enough monotone spanning trees in such graphs.

Approximation Schemes for Minimum 2-Connected Spanning Subgraphs in Weighted Planar Graphs

Quasi-polynomial time approximation schemes for the problems of finding the minimum-weight 2-edge-connected or biconnected spanning subgraph in planar graphs and a new greedy spanner construction for edge-weighted planarGraphs are presented.

Contraction decomposition in h-minor-free graphs and algorithmic applications

We prove that any graph excluding a fixed minor can have its edges partitioned into a desired number k of color classes such that contracting the edges in any one color class results in a graph of