The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit desi...The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.展开更多
We analyze a common feature of p-Kemeny AGGregation（p-KAGG） and p-One-Sided Crossing Minimization（p-OSCM） to provide new insights and findings of interest to both the graph drawing community and the social choice ...We analyze a common feature of p-Kemeny AGGregation（p-KAGG） and p-One-Sided Crossing Minimization（p-OSCM） to provide new insights and findings of interest to both the graph drawing community and the social choice community. We obtain parameterized subexponential-time algorithms for p-KAGG—a problem in social choice theory—and for p-OSCM—a problem in graph drawing. These algorithms run in time O＊（2O（√k log k））,where k is the parameter, and significantly improve the previous best algorithms with running times O.1.403k/and O.1.4656k/, respectively. We also study natural ＂above-guarantee＂ versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions of these problems are equivalent to a weighted variant of p-directed feedback arc set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of ＂votes＂ in the input to p-KAGG is odd the above guarantee version can still be solved in time O＊（2O（√k log k））, while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails（equivalently, unless FPT D M[1]）.展开更多
文摘The feedback vertex set (FVS) problem is to find the set of vertices of minimum cardinality whose removal renders the graph acyclic. The FVS problem has applications in several areas such as combinatorial circuit design, synchronous systems, computer systems, and very-large-scale integration (VLSI) circuits. The FVS problem is known to be NP-hard for simple graphs, but polynomi-al-time algorithms have been found for special classes of graphs. The intersection graph of a collection of arcs on a circle is called a circular-arc graph. A normal Helly circular-arc graph is a proper subclass of the set of circular-arc graphs. In this paper, we present an algorithm that takes time to solve the FVS problem in a normal Helly circular-arc graph with n vertices and m edges.
基金supported by a GermanNorwegian PPP grantsupported by the Indo-German Max Planck Center for Computer Science (IMPECS)
文摘We analyze a common feature of p-Kemeny AGGregation（p-KAGG） and p-One-Sided Crossing Minimization（p-OSCM） to provide new insights and findings of interest to both the graph drawing community and the social choice community. We obtain parameterized subexponential-time algorithms for p-KAGG—a problem in social choice theory—and for p-OSCM—a problem in graph drawing. These algorithms run in time O＊（2O（√k log k））,where k is the parameter, and significantly improve the previous best algorithms with running times O.1.403k/and O.1.4656k/, respectively. We also study natural ＂above-guarantee＂ versions of these problems and show them to be fixed parameter tractable. In fact, we show that the above-guarantee versions of these problems are equivalent to a weighted variant of p-directed feedback arc set. Our results for the above-guarantee version of p-KAGG reveal an interesting contrast. We show that when the number of ＂votes＂ in the input to p-KAGG is odd the above guarantee version can still be solved in time O＊（2O（√k log k））, while if it is even then the problem cannot have a subexponential time algorithm unless the exponential time hypothesis fails（equivalently, unless FPT D M[1]）.
