Danny Hermelin
Ben Gurion University, Industrial Engineering and Management, Faculty Member
Research Interests:
Research Interests:
ABSTRACT The Closest String problem asks to find a string s which is not too far from each string in a set of m input strings, where the distance is taken as the Hamming distance. This well-studied problem has various applications in... more
ABSTRACT The Closest String problem asks to find a string s which is not too far from each string in a set of m input strings, where the distance is taken as the Hamming distance. This well-studied problem has various applications in computational biology and drug design. In this paper, we introduce a new variant of Closest String where the input strings can contain wildcards that can match any letter in the alphabet, and the goal is to find a solution string without wildcards. We call this problem the Closest String with Wildcards problem, and we analyze it in the framework of parameterized complexity. Our study determines for each natural parameterization whether this parameterization yields a fixed-parameter algorithm, or whether such an algorithm is highly unlikely to exist. More specifically, let m denote the number of input strings, each of length n, and let d be the given distance bound for the solution string. Furthermore, let k denote the minimum number of wildcards in any input string. We present fixed-parameter algorithms for the parameters m, n, and k + d, respectively. On the other hand, we then show that such results are unlikely to exist when k and d are taken as single parameters. This is done by showing that the problem is NP-hard already for k = 0 and d ≥ 2. Finally, to complement the latter result, we present a polynomial-time algorithm for the case of d = 1. Apart from this last result, all other results hold even when the strings are over a general alphabet.
Research Interests:
Research Interests:
ABSTRACT The minimum linear arrangement (MLA) problem asks to embed a given graph on the integer line so that the sum of the edge lengths of the embedded graph is minimized. Most layout problems are either intractable, or not known to be... more
ABSTRACT The minimum linear arrangement (MLA) problem asks to embed a given graph on the integer line so that the sum of the edge lengths of the embedded graph is minimized. Most layout problems are either intractable, or not known to be tractable, parameterized by the treewidth of the input graphs. We investigate MLA with respect to three parameters that provide more structure than treewidth. In particular, we give a factor (1+ε)-approximation algorithm for MLA parameterized by (ε,k), where k is the vertex cover number of the input graph. By a similar approach, we describe two FPT algorithms that exactly solve MLA parameterized by, respectively, the max leaf and edge clique cover numbers of the input graph.
ABSTRACT The Steiner Multicut problem asks, given an undirected graph G, terminals sets T1,...,Tt $\subseteq$ V(G) of size at most p, and an integer k, whether there is a set S of at most k edges or nodes s.t. of each set Ti at least one... more
ABSTRACT The Steiner Multicut problem asks, given an undirected graph G, terminals sets T1,...,Tt $\subseteq$ V(G) of size at most p, and an integer k, whether there is a set S of at most k edges or nodes s.t. of each set Ti at least one pair of terminals is in different connected components of G \ S. This problem generalizes several graph cut problems, in particular the Multicut problem (the case p = 2), which is fixed-parameter tractable for the parameter k [Marx and Razgon, Bousquet et al., STOC 2011]. We provide a dichotomy of the parameterized complexity of Steiner Multicut. That is, for any combination of k, t, p, and the treewidth tw(G) as constant, parameter, or unbounded, and for all versions of the problem (edge deletion and node deletion with and without deletable terminals), we prove either that the problem is fixed-parameter tractable or that the problem is hard (W[1]-hard or even (para-)NP-complete). We highlight that: - The edge deletion version of Steiner Multicut is fixed-parameter tractable for the parameter k+t on general graphs (but has no polynomial kernel, even on trees). The algorithm relies on several new structural lemmas, which decompose the Steiner cut into important separators and minimal s-t cuts, and which only hold for the edge deletion version of the problem. - In contrast, both node deletion versions of Steiner Multicut are W[1]-hard for the parameter k+t on general graphs. - All versions of Steiner Multicut are W[1]-hard for the parameter k, even when p=3 and the graph is a tree plus one node. Hence, the results of Marx and Razgon, and Bousquet et al. do not generalize to Steiner Multicut. Since we allow k, t, p, and tw(G) to be any constants, our characterization includes a dichotomy for Steiner Multicut on trees (for tw(G) = 1), and a polynomial time versus NP-hardness dichotomy (by restricting k,t,p,tw(G) to constant or unbounded).
Research Interests:
Research Interests:
Research Interests:
Research Interests:
In this paper we use the notion of weak compositions to obtain polynomial kernelization lower-bounds for several natural parameterized problems. Let d��� 2 be some constant and let L 1, L 2���{0, 1}* x N be two parameterized problems... more
In this paper we use the notion of weak compositions to obtain polynomial kernelization lower-bounds for several natural parameterized problems. Let d��� 2 be some constant and let L 1, L 2���{0, 1}* x N be two parameterized problems where the unparameterized version of L 1 is NP-hard. Assuming coNP ⊈ NP/poly, our framework essentially states that composing t L 1-instances each with parameter k, to an L 2-instance with parameter k'��� t 1/dk O (1), implies that L 2 does not have a kernel of size O ( ...
Research Interests:
Research Interests:
Research Interests:
We give a novel characterization of W(1), the most important fixed-parameter intractability class in the W-hierarchy, using Boolean circuits that consist solely of majority gates. Such gates have a Boolean value of 1 if and only if more... more
We give a novel characterization of W(1), the most important fixed-parameter intractability class in the W-hierarchy, using Boolean circuits that consist solely of majority gates. Such gates have a Boolean value of 1 if and only if more than half of their inputs have value 1. Us- ing majority circuits, we define an analog of the W-hierarchy which we call the f W-hierarchy, and show that W(1) = f W(1) and W(t) � f W(t) for all t. This gives the first characterization of W(1) based on the weighted satisfiability problem for monotone Boolean circuits rather than anti- monotone. Our results are part of a wider program aimed at exploring the robustness of the notion of weft, showing that it remains a key param- eter governing the combinatorial nondeterministic computing strength of circuits, no matter what type of gates these circuits have.
Research Interests:
We show that three subclasses of bounded treewidth graphs are well-quasi-ordered by refinements of the minor order. Specifically, we prove that graphs with bounded feedback-vertex-set are well-quasi-ordered by the topological-minor order,... more
We show that three subclasses of bounded treewidth graphs are well-quasi-ordered by refinements of the minor order. Specifically, we prove that graphs with bounded feedback-vertex-set are well-quasi-ordered by the topological-minor order, graphs with bounded vertex-covers are well-quasi-ordered by the subgraph order, and graphs with bounded circumference are well-quasi-ordered by the induced-minor order. Our results give an algorithm for recognizing any graph family in these classes which is closed under the corresponding minor order refinement.
Research Interests:
The haplotype inference problem (HIP) asks to find a set of haplotypes which resolve a given set of genotypes. This problem is important in practical fields such as the investigation of diseases or other types of genetic mutations. In... more
The haplotype inference problem (HIP) asks to find a set of haplotypes which resolve a given set of genotypes. This problem is important in practical fields such as the investigation of diseases or other types of genetic mutations. In order to find the haplotypes which are as close as possible to the real set of haplotypes that comprise the genotypes, two models have been suggested which are by now well-studied: The perfect phylogeny model and the pure parsimony model. All known algorithms up till now for haplotype inference may find haplotypes that are not necessarily plausible, i.e., very rare haplotypes or haplotypes that were never observed in the population. In order to overcome this disadvantage, we study in this paper, a new constrained version of HIP under the above-mentioned models. In this new version, a pool of plausible haplotypes H is given together with the set of genotypes G, and the goal is to find a subset H ⊆ H that resolves G. For constrained perfect phlogeny hapl...
Research Interests:
In binary jumbled pattern matching we wish to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of size $i$ and has exactly $j$ 1-bits. The problem naturally generalizes to... more
In binary jumbled pattern matching we wish to preprocess a binary string $S$ in order to answer queries $(i,j)$ which ask for a substring of $S$ that is of size $i$ and has exactly $j$ 1-bits. The problem naturally generalizes to node-labeled trees and graphs by replacing "substring" with "connected subgraph". In this paper, we give an ${n^2}/{2^{\Omega(\log n/\log \log n)^{1/2}}}$ time solution for both strings and trees. This odd-looking time complexity improves the state of the art $O(n^2/\log^2 n)$ solutions by more than any poly-logarithmic factor. We obtain it by showing (1) A reduction from the string problem to computing min-plus matrix products using the recent seminal algorithm of Williams. (2) A black box reduction showing that any $O(n^{2-\varepsilon})$ algorithm for strings implies an $O(n^{2-\varepsilon'})$ algorithm for trees. Since currently $\varepsilon$ is non-constant, we now have $\varepsilon'=\varepsilon$.
Research Interests:
ABSTRACT The Longest Common Subsequence (LCS) of two or more strings is a fundamental well-studied problem which has a wide range of applications throughout computational sciences. When the common subsequence must contain one or more... more
ABSTRACT The Longest Common Subsequence (LCS) of two or more strings is a fundamental well-studied problem which has a wide range of applications throughout computational sciences. When the common subsequence must contain one or more constraint strings as subsequences, the problem becomes the Constrained LCS (CLCS) problem. In this paper we consider the Restricted LCS (RLCS) problem, where our goal is finding a longest common subsequence between two or more strings that does not contain a given set of restriction strings as subsequences. First we show that in case of two input strings and an arbitrary number of restriction strings the RLCS problem is NP-hard. Afterwards, we present a dynamic programming solution for RLCS and we show that this algorithm implies that RLCS is in FPT when parameterized by the total length of the restriction strings. In the last part of this paper we present two approximation algorithms for the hard variants of the problem.
Research Interests:
Research Interests:
ABSTRACT Kernelization is a strong and widely-applied technique in parameterized complexity. In a nutshell, a kernelization algorithm for a parameterized problem transforms a given instance of the problem into an equivalent instance whose... more
ABSTRACT Kernelization is a strong and widely-applied technique in parameterized complexity. In a nutshell, a kernelization algorithm for a parameterized problem transforms a given instance of the problem into an equivalent instance whose size depends solely on the parameter. Recent years have seen major advances in the study of both upper and lower bound techniques for kernelization, and by now this area has become one of the major research threads in parameterized complexity. We consider kernelization for problems on d-degenerate graphs, i.e. graphs such that any subgraph contains a vertex of degree at most d. This graph class generalizes many classes of graphs for which effective kernelization is known to exist, e.g. planar graphs, H-minor free graphs, H-topological minor free graphs. We show that for several natural problems on d-degenerate graphs the best known kernelization upper bounds are essentially tight. In particular, using intricate constructions of weak compositions, we prove that unless NP ⊆ coNP/poly: Dominating Set has no kernels of size O(k (d − 1)(d − 3) − ε ) for any ε > 0. The current best upper bound is \(O(k^{(d+1)^2})\). Independent Dominating Set has no kernels of size O(k d − 4 − ε ) for any ε > 0. The current best upper bound is O(k d + 1). Induced Matching has no kernels of size O(k d − 3 − ε ) for any ε > 0. The current best upper bound is O(k d ).
Research Interests:
Abstract. Multiple-interval graphs are a natural generalization of interval graphs where each ver- tex may,have more than one interval associated with it. Many applications of interval graphs also generalize to multiple-interval graphs,... more
Abstract. Multiple-interval graphs are a natural generalization of interval graphs where each ver- tex may,have more than one interval associated with it. Many applications of interval graphs also generalize to multiple-interval graphs, often allowing for more robustness in the modeling of the spe- ciflc application. With this motivation in mind, a recent systematic study of optimization problems in multiple-interval graphs
Research Interests:
Research Interests:
Research Interests:
In this work, we propose a compensated temperature pressure sensor fabricated on compound LiNbO3/Quartz/Quartz substrates obtained by Au/Au bonding at room temperature and double face lapping/polishing of LiNbO3/Quartz stack and a final... more
In this work, we propose a compensated temperature pressure sensor fabricated on compound LiNbO3/Quartz/Quartz substrates obtained by Au/Au bonding at room temperature and double face lapping/polishing of LiNbO3/Quartz stack and a final gold bonding with a structured Quartz wafer. This paper shows the possibility to obtain device which is intrinsically low sensitive to thermal effects, and even allowing a second