The complexity of dominating set reconfiguration

Suppose that we are given two dominating sets $D_s$ and $D_t$ of a graph $G$ whose cardinalities are at most a given threshold $k$. Then, we are asked whether there exists a sequence of dominating sets of $G$ between $D_s$ and $D_t$ such that each dominating set in the sequence is of cardinality at most $k$ and can be obtained from the previous one by either adding or deleting exactly one vertex. This problem is known to be PSPACE-complete in general. In this paper, we study the complexity of this decision problem from the viewpoint of graph classes. We first prove that the problem remains PSPACE-complete even for planar graphs, bounded bandwidth graphs, split graphs, and bipartite graphs. We then give a general scheme to construct linear-time algorithms and show that the problem can be solved in linear time for cographs, trees, and interval graphs. Furthermore, for these tractable cases, we can obtain a desired sequence such that the number of additions and deletions is bounded by $O(n)$, where $n$ is the number of vertices in the input graph

Reconfiguration of Cliques in a Graph

We study reconfiguration problems for cliques in a graph, which determine whether there exists a sequence of cliques that transforms a given clique into another one in a step-by-step fashion. As one step of a transformation, we consider three different types of rules, which are defined and studied in reconfiguration problems for independent sets. We first prove that all the three rules are equivalent in cliques. We then show that the problems are PSPACE-complete for perfect graphs, while we give polynomial-time algorithms for several classes of graphs, such as even-hole-free graphs and cographs. In particular, the shortest variant, which computes the shortest length of a desired sequence, can be solved in polynomial time for chordal graphs, bipartite graphs, planar graphs, and bounded treewidth graphs

A phase II study of cell cycle inhibitor UCN-01 in patients with metastatic melanoma: a California Cancer Consortium trial

Background Genetic abnormalities in cell cycle control are common in malignant melanoma. UCN-01 (7-hydroxystaurosporine) is an investigational agent that exhibits antitumor activity by perturbing the cancer cell cycle. A patient with advanced melanoma experienced a partial response in a phase I trial of single agent UCN-01. We sought to determine the activity of UCN-01 against refractory metastatic melanoma in a phase II study. Patients and methods Patients with advanced melanoma received UCN-01 at 90 mg/m2 over 3 h on cycle 1, reduced to 45 mg/m2 over 3 h for subsequent cycles, every 21 days. Primary endpoint was tumor response. Secondary endpoints included progression-free survival (PFS) and overall survival (OS). A two-stage (17 + 16), single arm phase II design was employed. A true response rate of ≥20% (i.e., at least one responder in the first stage, or at least four responders overall) was to be considered promising for further development of UCN-01 in this setting. Results Seventeen patients were accrued in the first stage. One patient was inevaluable for response. Four (24%) patients had stable disease, and 12 (71%) had disease progression. As there were no responders in the first stage, the study was closed to further accrual. Median PFS was 1.3 months (95% CI, 1.2–3.0) while median OS was 7.3 months (95% CI, 3.4–18.4). One-year and two year OS rates were 41% and 12%, respectively. A median of two cycles were delivered (range, 1–18). Grade 3 treatment-related toxicities include hyperglycemia (N = 2), fatigue (N = 1), and diarrhea (N = 1). One patient experienced grade 4 creatinine elevation and grade 4 anemia possibly due to UCN-01. No dose modification was required as these patients had disease progression. Conclusion Although well tolerated, UCN-01 as a single agent did not have sufficient clinical activity to warrant further study in refractory melanoma

Vertex Cover Reconfiguration and Beyond

Abstract. In the Vertex Cover Reconfiguration (VCR) problem, given graph G = (V,E), positive integers k and `, and two vertex cov-ers S and T of G of size at most k, we determine whether S can be transformed into T by a sequence of at most ` vertex additions or re-movals such that each operation results in a vertex cover of size at most k. Motivated by recent results establishing the W[1]-hardness of VCR when parameterized by `, we delineate the complexity of the problem restricted to various graph classes. In particular, we show that VCR re-mains W[1]-hard on bipartite graphs, is NP-hard but fixed-parameter tractable on graphs of bounded degree, and is solvable in time polyno-mial in |V (G) | on even-hole-free graphs and cactus graphs. We prove W[1]-hardness and fixed-parameter tractability via two new problems of independent interest.

Interactive Infrastructures: Physical Rehabilitation Modules for Pervasive Healthcare Technology

Traditional physical rehabilitation techniques are based mainly on mechanical structures and passive materials. This has certain limitations, which can be overcome by applying interactive technologies. As a team of designers, technologists and medical researchers and practitioners, we have developed an interactive sensor floor tile system and several other modules for rehabilitation exercises, as part of an interactive infrastructure to support rehabilitation. Since 2009, the team has advanced its understanding of rehabilitation practices and problems, and designed prototypes, interventions and demonstrators in order to gain feedback on our approach. We have identified as the three critical issues affecting rehabilitation motivation, customisation, andindependence. The system that we have developed is founded on the current mechanical practices, of improvisational nature, and creative use of existing materials and techniques, expanding from this way of working by applying new interactive digital technologies and 3D instant manufacturing techniques. We have developed a number of modules for the system, and a physical programming technique which aims to blend in with current practices. Two sets of sensor floor modules are in use in hospitals and we are reporting in this chapter the first positive effects the system has on the rehabilitation of stroke patients

The complexity of bounded length graph recoloring and CSP reconfiguration

In the first part of this work we study the following question: Given two k-colorings α and β of a graph G on n vertices and an integer ℓ, can α be modified into β by recoloring vertices one at a time, while maintaining a k-coloring throughout and using at most ℓ such recoloring steps? This problem is weakly PSPACE-hard for every constant k≥4. We show that the problem is also strongly NP-hard for every constant k≥4 and W[1]-hard (but in XP) when parameterized only by ℓ. On the positive side, we show that the problem is fixed-parameter tractable when parameterized by k+ℓ. In fact, we show that the more general problem of ℓ-length bounded reconfiguration of constraint satisfaction problems (CSPs) is fixed-parameter tractable parameterized by k+ℓ+r, where r is the maximum constraint arity and k is the maximum domain size. We show that for parameter ℓ, the latter problem is W[2]-hard, even for k=2. Finally, if p denotes the number of variables with different values in the two given assignments, we show that the problem is W[2]-hard when parameterized by ℓ−p, even for k=2 and r=3