Deciding Circular-Arc Graph Isomorphism in Parameterized Logspace

Deciding Monotone Duality and Identifying Frequent Itemsets in Quadratic Logspace

The monotone duality problem is defined as follows: Given two monotone formulas f and g in iredundant DNF, decide whether f and g are dual. This problem is the same as duality testing for hypergraphs, that is, checking whether a hypergraph H consists of precisely all minimal transversals of a simple hypergraph G. By exploiting a recent problem-decomposition method by Boros and Makino (ICALP 2009), we show that duality testing for hypergraphs, and thus for monotone DNFs, is feasible in DSPACE[log^2 n], i.e., in quadratic logspace. As the monotone duality problem is equivalent to a number of pro…

Canonical Representations for Circular-Arc Graphs Using Flip Sets

We show that computing canonical representations for circular-arc (CA) graphs reduces to computing certain subsets of vertices called flip sets. For a broad class of CA graphs, which we call uniform, it suffices to compute a CA representation to find such flip sets. As a consequence canonical representations for uniform CA graphs can be obtained in polynomial-time. We then investigate what kind of CA graphs pose a challenge to this approach. This leads us to introduce the notion of restricted CA matrices and show that the canonical representation problem for CA graphs is logspace-reducible to …

同态不可区分性、多重自动机等价性与多项式恒等检验

Homomorphism Indistinguishability, Multiplicity Automata Equivalence, and Polynomial Identity Testing

本文研究了同态不可区分性与多重自动机等价性问题，证明了其复杂度为C_L完全，并展示了算法在特定图类上的最优性。

Deciding Graph non-Hamiltonicity via a Closure Algorithm

We present a matching and LP based heuristic algorithm that decides graph non-Hamiltonicity. Each of the $n!$ Hamilton cycles in a complete directed graph on $n+1$ vertices corresponds with each of the $n!$ $n$-permutation matrices $P$, such that $p_{u,i}=1$ if and only if the $i^{th}$ arc in a cycle enters vertex $u$, starting and ending at vertex $n+1$. A graph instance ($G$) is initially coded as exclusion set $E$, whose members are pairs of components of $P$, $\{p_{u,i} ,p_{v,i+1}\}, i=1,n-1$, for each arc $(u,v)$ not in $G$. For each $\{p_{u,i} ,p_{v,i+1}\}\in E$, the set of $P$ satisfyin…