arXiv subjects

Jayme L. Szwarcfiter

Publications and source records attributed to Jayme L. Szwarcfiter.

24 records · Page 2Linked to original sources

arXiv2014

Towards a provably resilient scheme for graph-based watermarking

Digital watermarks have been considered a promising way to fight software piracy. Graph-based watermarking schemes encode authorship/ownership data as control-flow graph of dummy code. In 2012, Chroni and Nikolopoulos developed an ingenious such scheme which was claimed to withstand attacks in the form of a single edge removal. We extend the work of those authors in various aspects. First, we give a formal characterization of the class of graphs generated by their encoding function. Then, we formulate a linear-time algorithm which recovers from ill-intentioned removals of $k \leq 2$ edges, therefore proving their claim. Furthermore, we provide a simpler decoding function and an algorithm to restore watermarks with an arbitrary number of missing edges whenever at all possible. By disclosing and improving upon the resilience of Chroni and Nikolopoulos's watermark, our results reinforce the interest in regarding it as a possible solution to numerous applications.

cs.MM↗

arXiv2013

Exact algorithms for dominating induced matchings

Say that an edge of a graph G dominates itself and every other edge adjacent to it. An edge dominating set of a graph G = (V,E) is a subset of edges E' of E which dominates all edges of G. In particular, if every edge of G is dominated by exactly one edge of E' then E' is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to decide if it does admit is NP-complete. In this paper we consider the problem of finding a minimum weighted dominating induced matching, if any, of a graph with weighted edges. We describe two exact algorithms for general graphs. The algorithms are efficient in the cases where G admits a known vertex dominating set of small size, or when G contains a polynomial number of maximal independent sets.

cs.DM↗

arXiv2013

An $O^*(1.1939^n)$ time algorithm for minimum weighted dominating induced matching

Say that an edge of a graph $G$ dominates itself and every other edge adjacent to it. An edge dominating set of a graph $G=(V,E)$ is a subset of edges $E' \subseteq E$ which dominates all edges of $G$. In particular, if every edge of $G$ is dominated by exactly one edge of $E'$ then $E'$ is a dominating induced matching. It is known that not every graph admits a dominating induced matching, while the problem to decide if it does admit it is NP-complete. In this paper we consider the problems of finding a minimum weighted dominating induced matching, if any, and counting the number of dominating induced matchings of a graph with weighted edges. We describe an exact algorithm for general graphs that runs in $O^*(1.1939^n)$ time and polynomial (linear) space. This improves over any existing exact algorithm for the problems in consideration.

cs.DS↗

arXiv2012

Isomorphism of graph classes related to the circular-ones property

We give a linear-time algorithm that checks for isomorphism between two 0-1 matrices that obey the circular-ones property. This algorithm leads to linear-time isomorphism algorithms for related graph classes, including Helly circular-arc graphs, Γ-circular-arc graphs, proper circular-arc graphs and convex-round graphs.

cs.DS↗

arXiv2011

Subclasses of Normal Helly Circular-Arc Graphs

A Helly circular-arc model M = (C,A) is a circle C together with a Helly family \A of arcs of C. If no arc is contained in any other, then M is a proper Helly circular-arc model, if every arc has the same length, then M is a unit Helly circular-arc model, and if there are no two arcs covering the circle, then M is a normal Helly circular-arc model. A Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc graph is the intersection graph of the arcs of a Helly (resp. proper Helly, unit Helly, normal Helly) circular-arc model. In this article we study these subclasses of Helly circular-arc graphs. We show natural generalizations of several properties of (proper) interval graphs that hold for some of these Helly circular-arc subclasses. Next, we describe characterizations for the subclasses of Helly circular-arc graphs, including forbidden induced subgraphs characterizations. These characterizations lead to efficient algorithms for recognizing graphs within these classes. Finally, we show how do these classes of graphs relate with straight and round digraphs.

cs.DM↗

arXiv2010

Arboricity, h-Index, and Dynamic Algorithms

In this paper we present a modification of a technique by Chiba and Nishizeki [Chiba and Nishizeki: Arboricity and Subgraph Listing Algorithms, SIAM J. Comput. 14(1), pp. 210--223 (1985)]. Based on it, we design a data structure suitable for dynamic graph algorithms. We employ the data structure to formulate new algorithms for several problems, including counting subgraphs of four vertices, recognition of diamond-free graphs, cop-win graphs and strongly chordal graphs, among others. We improve the time complexity for graphs with low arboricity or h-index.

cs.DS↗