Eun Jung Kim

We present a linear-time algorithm to compute a decomposition scheme for graphs G that have a set X ⊆ V ( G ), called a treewidth-modulator , such that the treewidth of G − X is bounded by a constant. Our decomposition, called a protrusion decomposition , is the cornerstone in obtaining the following two main results. Our first result is that any parameterized graph problem (with parameter k ) that has a finite integer index and such that Y es -instances have a treewidth-modulator of size O ( k

Designing energy-efficient clusters has recently become an important concern to make these systems economically attractive for many applications. Since the cluster interconnect is a major part of the system, the focus of this paper is to characterize and optimize the energy consumption in the entire interconnect. Using a cycle-accurate simulator of an InfiniBand Architecture (IBA) compliant interconnect fabric and actual designs of its components, we investigate the energy behavior on regular an

The InfiniBand/sup TM/ Architecture (IBA) is envisioned to be the default communication fabric for future system area networks (SAN). However, the released IBA specification outlines only higher level functionalities, leaving it open for exploring various design alternatives. In this paper we investigate four co-related techniques to provide high and predictable performance in IBA. These are: (i) using the shortest path first (SPF) algorithm for deterministic packet routing; (ii) developing a mu

A chordless cycle, or equivalently a hole, in a graph G is an induced subgraph of G which is a cycle of length at least 4. We prove that the Erdős-Pósa property holds for chordless cycles, which resolves the major open question concerning the Erdős-Pósa property. Our proof for chordless cycles is constructive: in polynomial time, one can find either k+1 vertex-disjoint chordless cycles, or c1k2log⁡k+c2 vertices hitting every chordless cycle for some constants c1 and c2. It immediately implies an

We show a flow-augmentation algorithm in directed graphs: There exists a randomized polynomial-time algorithm that, given a directed graph G, two integers s,t ∈ V(G), and an integer k, adds (randomly) to G a number of arcs such that for every minimal st-cut Z in G of size at most k, with probability 2−poly(k) the set Z becomes a minimum st-cut in the resulting graph.

We present an undirected version of the recently introduced flow-augmentation\ntechnique: Given an undirected multigraph $G$ with distinguished vertices $s,t\n\\in V(G)$ and an integer $k$, one can in randomized $k^{O(1)} \\cdot (|V(G)| +\n|E(G)|)$ time sample a set $A \\subseteq \\binom{V(G)}{2}$ such that the\nfollowing holds: for every inclusion-wise minimal $st$-cut $Z$ in $G$ of\ncardinality at most $k$, $Z$ becomes a minimum-cardinality cut between $s$ and\n$t$ in $G+A$ (i.e., in the multi